Due to the intermittent nature of wind, the wind power output tends to be inconsistent, and hence maximum power point tracking (MPPT) is usually employed to optimize the power extracted from the wind resource at a wide range of wind speeds. This paper deals with the rotor speed control of a 2 MW direct-driven permanent magnet synchronous generator (PMSG) to achieve MPPT. The proportional-integral (PI), proportional-derivative (PD), and proportional-integral-derivative (PID) controllers have widely been employed in MPPT studies owing to their simple structure and simple design procedure. However, there are a number of shortcomings associated with these controllers; the trial-and-error design procedure used to determine the P, I, and D gains presents a possibility for poorly tuned controller gains, which reduces the accuracy and the dynamic performance of the entire control system. Moreover, these controllers’ linear nature, constricted operating range, and their sensitivity to changes in machine parameters make them ineffective when applied to nonlinear and uncertain systems. On the other hand, phase-lag compensators are associated with a design procedure that is well defined from fundamental principles as opposed to the aforementioned trial-and-error design procedure. This makes the latter controller type more accurate, although it is not well developed yet, and hence it is the focus of this paper. The simulation results demonstrated the effectiveness of the proposed MPPT controller.
The increasing energy demand across the globe has led to an enormous interest in the cost-competitive, environmental friendly, and reliable renewable energy (RE) technologies to complement the conventional methods of generating electricity [
This will aid in achieving the grid compliance of the WECS in terms of the voltage level, frequency, active power, and reactive power [
The direct-driven PMSG-based WECS [
The ability of a variable speed WT to extract optimal power at a wide range of wind speeds makes it possible to be operated in the MPPT mode [
The direct (power angle) control and vector-oriented control (VOC) are the well-developed control techniques used to perform the independent control of active and reactive power in grid-connected WECS and they are discussed further in [
Controllers are mainly incorporated into a system to improve the overall performance and stability of the system. This is done to meet certain design specifications such as percentage overshoot, rise time, settling time, phase margin, and a specified bandwidth [ Proportional-derivative (PD), proportional-integral (PI), and proportional-integral-derivative (PID) Phase-lag compensator, phase-lead compensator, and lag-lead compensator
Currently, PI, PD, and PID controllers are widely used in academia and in industrial control systems because they have a simple structure and simple design procedure and they are cost-effective [
On the other hand, phase-lead, phase-lag, and lag-lead compensators are associated with a design procedure that is well defined from fundamental principles as opposed to the trial-and-error design procedure. Moreover, the initial performance of the uncompensated system is taken into consideration prior to the controllers’ modeling and design. The compensators are designed in the frequency domain to achieve the desired design specifications using bode plots and step-response curves. This makes the latter design procedure more accurate.
The literature review has shown that more focus has been put on employing PI controllers in several MPPT control studies for both DFIG-based and PMSG-based WECSs. However, although there have been a few studies on implementing phase-lag compensators in different control applications, particularly in DFIG-based WECS for low voltage ride through control by Wang et al. [
The research investigation discussed in this paper is motivated by a community-run wind power mini generation pilot project which is implemented in Lüderitz, a coastal town located in the southwestern Namibia, along the Namib Desert [
The mechanical power extracted from the wind resource by the wind turbine is given by the following equation [
The dynamic modeling of a PMSG is normally carried out in the direct-quadrature (
In the frequency domain, the gain and phase margins are the important indicators of system robustness, performance, and stability and hence they are widely used for controller designs. Phase and gain margins are determined by using Bode plots of the system’s open-loop transfer functions. A gain margin is referred to as the amount of additional open-loop gain, expressed in decibels (dB), which is needed to make the closed-loop system unstable. The phase margin is referred to as the additional open-loop phase shift which is needed at unity gain to make the closed-loop system unstable [
Graphical representation of the gain and phase margin and their corresponding crossover frequencies.
The phase-lead compensator improves the performance of the open-loop system by adding a phase boost to the phase curve to obtain the desired phase margin at the desired gain crossover frequency [
Magnitude and phase curves: (a) phase-lead compensator and (b) phase-lag compensator.
The lag-lead compensator combines the features and functions of the phase-lead and phase-lag compensators. Therefore, it is just a series connection of the two compensators.
Controllers are mainly incorporated into a system to improve the overall performance and stability of the system. This is done to meet certain design specifications such as percentage overshoot, rise time, settling time, phase margin, and a specified bandwidth [
The percentage overshoot refers to the amount by which the waveform overshoots the steady-state value at peak time. It is related to the damping ratio
The phase margin is related to the damping ratio by the following equation [
The natural frequency of the system is related to the specified bandwidth and damping ratio by the following equation [
The settling time of the controller is related to the system’s natural frequency and damping ratio by the following equation [
The rise time of the controller is related to the system’s natural frequency and damping ratio by the following equation [
The maximum power point tracking (MPPT) is achieved by the machine-side converter (MSC) controller. This is done by adjusting the generator speed relative to the change in the wind speed. Figure
Schematic diagram of the PMSG-based WECSs.
Figure
Block diagram of a typical converter controller.
Figures
Inner current control loop for the generator-side converter: (a) initial control loop and (b) final control loop.
A converter is usually considered as an ideal transformer with a time delay caused by the switching of the converter switches. The delay time is equal to the half of the switching time. The transfer function of the converter block is therefore given by the following equation [
The system’s behavior is governed by the equations that represent the PMSG’s stator voltages in
Taking the Laplace transformation of (
From Figure
To prevent the ripple generated during the switching of the pulse width modulation (PWM) converter switches from affecting the controller’s performance, it is recommended that the inner current controller’s bandwidth should be as wide as possible and at least be less than or equal to one-fourth of PWM converter’s switching frequency [
Considering the wind turbine’s rated line-to-line voltage of 690 V as given in Table
Figure
Bode plot of the uncompensated open-loop transfer function.
It is observed that the phase margin and bandwidth of the uncompensated system are 88.2° and 635 rad/s, respectively. The bandwidth is too low as compared to the desired value of
To obtain the desired bandwidth, the system’s open-loop transfer function needs to be multiplied by a gain
Multiplying (
Figure
Bode plot of the gain-compensated transfer function.
Phase attenuation =
The phase attenuation is used to locate the pole
The phase-lag compensator is applied to the gain-compensated system, and hence multiplying (
Figure
Bode plot of the phase-lag compensated transfer function.
It is observed that the phase-lag compensator shifted the phase curve down to yield the phase margin of 39.5°. The bandwidth is maintained at
Figures
Step response of the inner current controller’s closed-loop transfer function: (a) peak response, (b) settling time, and (c) rise time.
Figure
This illustrates that the settling time design specification of the inner current controller has been achieved. Figure
The outer control loops are expected to be slower than the inner current control loops. Therefore, the bandwidth of the outer control loops is taken to be 625 Hz (3926.99 rad/s), which is one-fourth of the inner current control loops’ switching frequency. Moreover, the slower outer loop needs to have a smaller overshoot as compared to the fast inner current controllers loop to get rid of as many oscillations in the controller as possible, thereby enhancing the stability of the entire system. Therefore, the percentage overshoot is taken to be 5%. Therefore, the damping ratio and phase margin calculated using (
The output power
MPPT control loop: (a) initial control loop and (b) final control loop.
Using the
In stator voltage reference frame,
Therefore, the system transfer function in Figure
From Figure
Figure
Bode plot of the uncompensated transfer function.
From Figure
Gain magnitude at the desired bandwidth.
The magnitude at the desired crossover frequency is then used to calculate the attenuation
The frequencies where the pole
Therefore, the pole
Multiplying (
Figure
Bode plot of the phase-lag compensated transfer function.
From Figure
Phase attenuation =
Therefore, the frequency [Hz] where the pole
The transfer function of the phase-lag compensator is given by the following equation:
The second phase-lag compensator is applied to the phase-lag compensated system, and hence multiplying (
Figure
Bode plot of the transfer function compensated with the two phase-lag compensators.
Figures
Step response of the MPPT controller’s closed-loop transfer function: (a) peak response, (b) settling time, and (c) rise time.
Figure
The proposed wind turbine conversion system has been implemented in PSIM software package as shown in Figure
Proposed wind energy conversion system.
Tables
Wind turbine parameters.
Parameters | Values |
---|---|
Rated power (MW) | 2 |
Cut-in wind speed (m/s) | 4 |
Rated wind speed (m/s) | 13 |
Cut-out wind speed (m/s) | 25 |
Number of rotor blades | 3 |
Rotor area (m2) | 4587 |
Rotor diameter (m) | 76.42 |
Air density (kg/m2) | 1.225 |
Optimal power coefficient |
0.4 |
PMSG parameters.
Parameters | Value |
---|---|
Generator type | PMSG |
Rated mechanical power, |
2 |
Rated apparent power, |
2.24 |
Rated |
690 (rms) |
Rated power factor, pf | 0.89 |
Rated rotor speed, |
22.5 |
Pole pairs, |
26 |
Rated mechanical torque (kNm) | 848.83 |
Flux linkage, |
4.971 |
Stator winding resistance, |
0.821 |
Stator |
1.573 |
Stator |
1.573 |
The wind speed is varied to analyze how the system reacts to the change in wind speed. Figure
Wind speed model.
Figures
MPPT control: (a) rotor angular speed, (b) aerodynamic power, and (c) aerodynamic torque.
Figure
This research investigation serves as a starting point of modularly expanding the already existing mini wind power plant in Namibia by thoroughly analyzing and designing the rotor speed controller of a 2 MW PMSG-based WECS to achieve MPPT.
The wind turbine system components and the MPPT controller were successfully implemented in PSIM software package. The design and stability analysis of the generator-side converter controller which comprises a phase-lag compensator was carried out in MATLAB software package using bode plots and step-response curves. Based on the simulation results, it was observed that the MPPT controller enabled the power generated from the WT to closely track the optimal power curve to ensure maximum power generation when the wind speed is less than the WT’s rated wind speed (13 m/s). It was also observed that when the wind speed is equal to the WT’s rated wind speed, the aerodynamic power generated is equal to 2 MW which is the WT’s rated power. The MPPT controller also enabled the generated torque to closely track the optimal torque curve when the wind speed was lower than the WT’s rated wind speed.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research is supported by the Eskom Power Plant Engineering Institute (EPPEI) Program.