2. Modeling and simulation of PMSG-based WECS

The configuration and control schematic of PMSG-based WECS are depicted in Figure 1. The captured kinetic energy of wind rotates the generator rotor and cuts the magnetic field set by the stator and thus produces electric power. The generated AC output voltage is converted into DC using bridge rectifier, and again back to AC by means of DC/AC inverter. A DC-link voltage is connected in between the generator and grid-side converters/inverters.

Figure 1. Configuration and control logic used in PMSG-based WECS.

Voltage-fed, current-controlled inverter with insulated-gate bipolar transistor (IGBT) as a switching device is used to control and synchronize both the stator output voltage and frequency with the grid components. The stator voltage is stepped up by a transformer and passed to the network through a point of common coupling (PCC) where the injection of wind power has an impact on voltage magnitude, its flicker, and its output waveform. The magnetic core losses are minimized by the inclusion of a transformer to increase the overall efficiency.

This section presents several modules like model of PMSG, a model of rectifier, a model of boost converter, and a voltage-fed inverter model with SVPWM along with voltage vectors. The major system variables continuously monitored and controlled generate optimal power at different wind speeds by PMSG and thus active and reactive power are injected into the grid and to the DC bus.

The control of rectifiers and converters is done by sinusoidal PWM control technique at the generator-side control, while the grid-side inverter control includes SVM technique. The dynamic model of PMSG with its rotor speed control system is represented by the equations of generator in a reference coordinates system rotating synchronously with the magnetic flux. Since the stator current vector is represented by rotor flux with respect to d-q axis reference system, id, iq and the electromagnetic torque are related with each other through this vector. The magnetic axis of the rotor is fixed as reference for spatial orientation of fictitious rotor windings.

Considering the inductances Lds and Lqs in the stator of the generator which are equal along the direct and quadrature axes, respectively and Lds = Lqs = Ls at steady-state condition, the stator equations in terms of d and q axes are given in Eqs. (1) and (2) as

$$\frac{d\dot{q}\_{\rm ds}}{dt} = \frac{1}{L\_{\rm ds} + L\_{\rm ls}}(-R\_{\rm s}\dot{q}\_{\rm ds}) + \omega\_c (L\_{\rm qs} + L\_{\rm ls})\dot{q}\_{\rm qs} + u\_d \tag{1}$$

$$\frac{d\dot{\imath}\_{qs}}{dt} = \frac{1}{L\_{qs} + L\_{ls}} \left( -R\_s \dot{\imath}\_{sq} \right) - \omega\_c \left( (L\_{ds} + L\_{ls}) \dot{\imath}\_{ds} + \frac{d\psi}{dt} ds \right) + u\_q \tag{2}$$

where Lls is the leakage inductance of the stator referred to d and q axes.

PMSG is modeled by using derived mathematical equations and simulated using SimPower Systems library available in MATLAB/Simulink. The simulation is carried out for a gridconnected PMSG in both open- and closed-control modes. Each and every individual model is integrated to analyze the complete system behavior. Since wind power is unreliable, the PMSG output is not stable. Hence, to synchronize the generated output voltage with the inverter frequency, PLL is used. The generator is directly connected to the grid through a fullscale back-to-back power converter.

The power converter decouples the generator and the grid. In addition, this full-scale power converter allows full controllability of the entire system. Both the generator/machine and gridside converters operate in rectifier or inverter mode and thus maintain the bidirectional power flow. The generated three-phase AC voltage is stepped up and passed through the utility grid. The generator/stator-side converter mainly controls the speed of generator to obtain the maximum power output even at low wind speeds. The grid-side inverter maintains DC-link capacitor voltage constant and controls the reactive power delivered to the grid. The DC link

created by the capacitor in the middle is required to sustain stabilized generator output to connect the power grid through an inverter circuit. It decouples the operation of both the converters, thus allowing their design and operation suits for optimization. The full-scale back-to-back converter makes constant voltage possible and fixed frequency on grid side though the rotor runs at varying speeds. The two back-to-back converters are controlled independently through decoupled d-q vector control approach.

A three-phase permanent magnet synchronous machine with sinusoidal back EMF of rated capacity 12 kW, 560 V, and 1700 rpm has been taken for analysis. The average wind speed is set as 9 m/s and subject to change between 5 and 12 m/s; it is done by either setting the limits in the saturation block or setting the limits of step input. The outputs of this block are mechanical torque Tm, mechanical power Pm, power coefficient Cp, and the tip speed ratio Z. The mechanical torque is multiplied with gain to get an electrical torque. The electromagnetic torque developed is the main source of input to rotate the PMS generator and hence to measure phase currents in the rotor terminals. It includes subsystems of PMSG with its rectifier circuit, a three-phase uncontrolled diode full-bridge type. The performance of PMSG with its steady-state and transient-state parametershas been analyzed for both open-loop and closed-loop control modes in the following sections.

As PMSG is a variable speed generator and coupled with the wind turbine without gearbox, it is not that much difficult to control the rotor speed in open-loop control method. The generator model is represented in synchronously rotating d-q reference frame. The back-to-back voltage source converters (VSC) are controlled independently through decoupled d-q vector control method. The generator-side converter regulates the speed of PMSG to implement MPPT control, that is, the electromagnetic torque of PMSG is controlled with respect to generator speed such as to achieve maximum power point. The speed control is realized through field orientation where the q-axis current is used to control the rotational speed of the generator with respect to the varying wind speed. In order to obtain maximum torque per ampere and to minimize the resistive losses in generator, the d-axis current is set to zero, while the q-axis current reference is determined by the power controller. A random source with multiplier is used to adjust wind speed to get 12–15 m/s. The model of PMSG in open-loop control mode with rectifier and two boost converters along with the inverter has been shown in Figure 2.

The magnitude of output voltage at stator terminals increases and the generated stator voltage is used to meet the load demand. The DC-link voltage in the intermediate stages is boosted up and measured. Whenever there is a low wind speed, back-to-back power converter draws more power from the grid to drive the generator such as to provide high startup torque. This converter decouples the wind turbine and grid, regulates the operational speed of wind turbine generator, and controls the active and reactive powers injected into the grid, thus improving the power quality.

As the voltage and frequency of generator output change along with the variations of wind speed change, the generator-side boost converter is used to track the maximum wind power. To maintain a constant switching frequency within the converter, the d- and q-axis currents are controlled indirectly through a current-regulated voltage source PWM converter. The d-q voltage control signals of the converter are obtained by comparing the d- and q-axis reference currents with the actual d- and q-axis currents of the stator. Final control action is done with dand q-axis voltage control signals. Thus, generator/machine-side converter controls PMSG to achieve optimum energy extraction from the wind.

Figure 2. Model of PMSG-based WECS in open-loop control.
