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Posted on 30 January 2019

Multi-Physical Domain Modeling of a DFIG Wind Turbine System using PLECS® Simulation Software

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Power conversion systems comprise several physical domains including electrical, magnetic, thermal, and often mechanical subsystems. To fully understand the behavior of the overall system prior to construction, and therefore increase likelihood of a successful design, the characteristics of the individual domains and their effects on the power converters must be taken into account. PLECS is a simulation tool developed for power electronics engineers that allows for very efficient and robust modeling of such systems with multi-physical domains and associated controls. In this study, a 2MW grid-connected wind power generation system has been designed in detail using PLECS, and the effects of the multi-domain interactions are investigated.

By Min Luo, Plexim GmbH and Kristofer Eberle, Plexim Inc.

Introduction

A cost effective method of wind power generation is to connect the output of the turbine to a doubly-fed induction generator (DFIG), allowing operation at variable speeds while minimizing the losses, cost and size of the power converters. A DFIG wind turbine system has a complex design involving multiple physical domains strongly interacting with each other. The electrical system, for instance, is influenced by the converter’s cooling system and mechanical components, including rotor blades, shaft and gearbox. The influence of domains on one another must be considered in order to achieve an optimized overall system performance.

In addition to creating an accurate model of the entire system, it is also important to model the real-world operating and fault conditions. For fast prototyping and performance prediction, computer-based simulation has been widely adopted in the engineering development process. Modeling such complex systems while including switching power electronic converters requires a powerful and robust simulation tool. Furthermore, a rapid solver is critical to allow for developing multiple iterative enhancements based on insight gained through system simulation studies.

System modeling of a wind turbine in PLECS

A 2 MW DFIG wind turbine model has been developed in PLECS and a demonstration is shown in Fig. 1.

Schematic of the DFIG wind turbine model in PLECS

The components of the system are taken from PLECS’ different physical domain libraries, including the electrical, magnetic, and mechanical, as well as signal processing and control systems categories.

Electromagnetic system

The electrical domain is used to accurately model the grid, power converters and electric machine. The machine’s stator terminals are directly connected to the medium-voltage grid via a three-winding transformer and transmission line. The rotor is connected to the transformer via two back-to-back AC-DC converters with a common DC-link. A brake resistor is included to discharge the DC-link capacitor in the event of an overvoltage condition. The rotor-side inverter is directly connected to the induction machine’s rotor, while the grid-side inverter is connected to the tertiary winding of the transformer through an LCL filter to meet current THD standards for grid connection. Multi-legged coupled magnetic structures, such as the transformer in this application, can be difficult to represent with an electrical equivalent circuit. Magnetic modeling in PLECS1 offers a powerful method for modeling such components by directly capturing a magnetic circuit using windings and lumped core parts with user-specified geometries. Compared to a co-simulation with a finite element analysis (FEA) tool, which results in significant simulation times, this lumped magnetic circuit method is able to integrate magnetic component models into a system level simulation without causing any substantial increase in the duration. The PLECS magnetic domain is also capable of handling more complex effects including nonlinearities caused by saturation and hysteresis. In addition, the separation of electrical and magnetic domains provides the user a clearer overview when approaching the actual hardware construction.

A Wye-Wye-Delta connected three-leg iron core transformer with laminated material is designed and each leg is modeled as a magnetic permeance. The complete model is shown in Figure 2, where the linear permeance core components can be replaced by permeances with saturation or permeances with hysteresis to simulate nonlinear effects.

Transformer model in the PLECS magnetic domain

In this case, Eddy current power losses are represented by magnetic resistance components, which are series-connected to the permeances. Leakage fields are modeled with leakage permeances connected in parallel to the windings and the winding components serve as the interface between the electrical and magnetic domains.

Cooling system and device thermal modeling

Semiconductor power losses play an important role in the converter design and can be investigated using PLECS’ thermal domain2. The PLECS ideal switch approach yields fast and robust simulations. Accurate conduction and switching loss calculations are obtained via look-up tables that are easily populated with values from data sheets. The dependence of temperature in determining power losses can be established, and the thermal energy transfer characteristics from the junction to the case can be specified.

The PLECS heat sink component absorbs the power losses produced by the components that it borders. It feeds these losses to the cooling system, which is simply modeled in this case as a thermal resistance and a constant temperature sink (ambient temperature). During the simulation, the junction temperature of the IGBTs can be monitored to ensure the cooling system is properly sized. Major and minor temperature cycles of the semiconductor dies can be used for life and reliability analyses.

Mechanical system

Variations of the aerodynamic torque on the blades and, consequently, electrical torque on the induction machine’s rotor are propagated to the wind turbine’s drivetrain. Rotational speed fluctuations can lead to disturbances in the electrical domain, which depends critically on drivetrain torsional characteristics to damp out oscillations. This model uses a wind source to perturb the mechanical system in order to investigate the effects of such system resonances. A wind torque input depending on wind speed and propeller rotational speed is provided. The three blades transfer the wind torque to the hub shaft, which is connected to a gearbox. Using a specific gear ratio the gearbox increases the rotational speed of the hub shaft onto the induction machine’s rotor shaft. The coupling between the components experiences elastic and damping effects due to its material characteristics. Friction also occurs on the bearings, leading to additional power losses. The mechanical portion of this model includes components representing inertias, masses, a gearbox, shaft elasticity and damping, and friction, as shown in Figure 3.

Complete drivetrain modeled in the PLECS mechanical domain

Control system design

The back-to-back converter comprises separate machine-side and grid-side portions, connected via a DC-link capacitor. The machine side converter regulates the DFIG torque and thus the rotational speed with a double loop structure, where the outer speed loop generates the reference signal for the inner current loop. In addition, the machine-side converter regulates the DFIG reactive power injection. The grid-side converter transfers the active power from the machine side converter into the grid through an LCL filter, and maintains the DC-link voltage. The methods of active damping, feedforward, and integrator anti-windup are adopted for the PI controllers, and the converters operate using space vector pulse-width modulation (SVPWM). The current control loop is synchronized with the grid voltage, where the orientation reference is provided by a phase-locked loop (PLL). In a real wind turbine system, the turbine power controller often uses a maximum power point tracking (MPPT) scheme to provide the reference signal for the speed controller. In this case, an MPPT scheme is not modeled considering the relatively short time range of the simulation and a constant value is instead given as the speed reference.

Simulation schemes

The following example scenarios can be studied through simulation:

Initial state: At simulation start, the generator operates at synchronous speed to the grid frequency. Most of the generated active power is injected into the grid via the stator winding of the induction machine, while due to the zero slip condition, virtually no power flows through the rotor except for the resistive losses. The reactive power generation is not activated yet at this stage.

Acceleration: The rotation speed of the turbine is accelerated via a step jump on the reference input of the speed controller, to achieve maximum power generation under a given wind speed.

Grid fault: A three-phase short circuit fault (zero voltage sag condition) occurs on the medium-voltage grid and the interaction between the grid, converters, and control systems can be studied immediately after.

Results and discussion

By simulating such scenarios described above, the robustness of the design is observed and improvements can be made, namely with the control techniques. The various parameters in the system are chosen to provide desirable results during the entire operating range of the turbine. At the start of the simulation, a damped oscillation can be observed due to the elastic and lossy coupling between the mechanical parts. After a period of acceleration, the electrical torque of the induction machine and the wind torque enter a balanced state and the rotational speed remains constant.

A grid-side fault known as “low voltage ride through” (LVRT) behavior is investigated by reducing the grid voltage. The electrical transient during the grid fault is shown in Figure 4.

Electrical, thermal and mechanical transient during the grid fault

The AC current exhibits a large peak immediately after the fault occurs, and then is maintained below a certain range because of the saturated input of the current controller. Due to the voltage drop at the transformer tertiary winding, the grid-side inverter is also no longer able to transfer power, so the DC-link voltage is nearly uncontrolled in the first seconds after the fault. The DC-link capacitor is then charged or discharged purely by the machine-side inverter. The voltage is clamped to a safe level due to the activation of the chopper circuit. The capacitor is discharged as the grid voltage recovers and the grid-side inverter is again able to transfer enough power.

Conclusion

The modeling and simulation of a complete DFIG wind turbine model has been presented in this article. The same model is packaged as a PLECS demo model and can be further explored using the Demo Mode of PLECS Standalone. To obtain this free download, visit Plexim’s website (www.plexim.com). With the help of PLECS, the transient effects from multiple physical domains can be evaluated in a single system model without requiring excessive simulation times, thereby providing an effective and accurate means for investigating and addressing issues related to inter-physical domain interactions. Such fully integrated models provide power electronic designers with more insight into the system before hardware is built, leading to time and cost savings.

References
[1] J. Allmeling, W. Hammer, and J. Schö nberger, “Transient simulation of magnetic circuits using the permeance-capacitance analogy,” in Control and Modeling for Power Electronics (COMPEL), IEEE 13th Workshop on, 2012.
[2] J. Schönberger, “Predicting device thermal performance using a simulation tool,” Bodo’s Power News, pp. 38–40, February 2009.

 

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