1. Introduction
After decades of development, the concern level about wind power research and application is still escalating. Being a clean and renewable energy resource, the wind power generator system extracts kinetic energy transforming into electrical form. While the wind energy source is apposite to provide the utility grid, small power wind systems can be used mostly as local distributed energy sources or one part of a microgrid since it is easy to be implemented and maintained. The scale of small power is defined by the power production level. In the United States of America, the wind energy system products lower than 100 kW are named small power wind systems; but, the criterion in Europe is 50 kW [
1,
2]. Due to its small size and light weight as well as its advances in aspects of reliability, energy density, and efficiency, the most used small power wind generator is the permanent magnet synchronous machine (PMSM) [
3,
4].
The small power wind energy system usually operates at maximum power point tracking (MPPT) case when wind velocity is lower than rated wind velocity; and constant power output is demanded when wind velocity is over rated wind velocity. However, being the local distributed energy source or a part of microgrid, the small scale wind energy system can also be required for the power limited control (PLC) case, at the range lower than rated wind velocity. Consequently, a general control strategy which could deal with both MPPT and PLC cases is necessary to be implemented.
As discussed and presented in [
5], the wind kinetic energy is converted into DC electrical energy by means of three possible solutions: the passive electrical structure using a three-phase diode bridge; the active structure using a controllable AC–DC converter; or the active structure using a controllable DC–DC converter with the three-phase diode bridge. Considering the energy conversion efficiency the tendency to decrease the financial cost, the active structure using DC–DC converter presented in [
5] was selected in this paper.
Several approaches for MPPT [
3,
4,
5,
6,
7,
8,
9,
10,
11] and PLC [
12,
13,
14,
15,
16] have been accomplished. Briefly, MPPT algorithms can be sorted into indirect and direct methods as summarized in [
3,
4]. The former type, indirect methods, indicates that the method relies on a precise mathematical model of the studied system. In [
6], the ratio between the electrical output power and the value of DC voltage cube and the ratio between the DC current and the value of the DC voltage square are regarded as constant for all maximum power operating points. Based on these references, the DC voltage is controlled by a proportional-integral (PI) controller with a DC–AC converter at the grid side, while the rotational speed is controlled by another PI controller with an AC–DC converter at the generator side. In [
7], the authors used the power coefficient (
) to make a lookup table to supply the reference of the mechanical rotational speed for different wind velocities. Also, this paper used electrical variables three-phase voltages estimating the rotational speed to avoid the usage of mechanical sensors. Both of these two indirect MPPT methods require pre-knowledge of studied system, and are sensitive to the parameter drift, which has not been discussed in these articles. Relatively, the direct method, such as the perturb and observe (P&O) principle used in [
5,
8] injects operating state disturbance into the system, and based on the system response, it determines the further direction of the variation of system operating point. Different from [
5], in [
8] it is considered only the mechanic inertia of generator, which is just 0.016 kg·m
2, thus the effect of the actually sluggish mechanic inertia of wind blades has been ignored. The direct MPPT method based on the P&O method presents more robustness and flexibility than the indirect method, since it does not require the mathematical model of the objective. However, the direct method usually asks designers with a good know-how level to make a tradeoff between response rapidity and stability. Some advanced algorithms such as the Neural Networks [
9] can be used to estimate wind velocity or mechanical rotational speed and to establish a mathematical model of the system trained by a Particle Swarm Optimization method. This combination can avoid the requirement of expensive mechanical sensors and supply a highly precise model of the studied system; but the process of training the Neural Networks demands lots of preliminary work. The application of some advanced controlling techniques, such as the extended Kalman filter [
10,
11] also has been implemented for MPPT. Those techniques improved performances while increasing the complexity of application of those MPPT methods.
The integrated control strategy of output power also has many approaches [
12,
13,
14,
15,
16]. In [
12], the authors use the variable step-size P&O method, which involves a sectional defined function modifying the output current of DC–DC converter to realize MPPT and a PI controller to realize PLC. Since [
12] did not demonstrate the experimental verification, neither the power level of system nor the effect of the mechanical inertia are validated. Therefore, it is hard to determine if this combination is suitable to the small scale wind generator or not. In [
13], a modified P&O method is selected for MPPT regulation. However, in this paper, PLC just means the constant power output when wind velocity is over the rated value of the studied system; in addition, a double loop PI control with a voltage inner loop and a power outer loop is implemented to achieve this objective. However, the inertia, combining the generator and the emulator of wind velocity and blades, is determined as 0.03 kg·m
2, which does not match the reality of real wind turbines. Thus, it means that [
13] has not considered the influence of mechanical inertia which is an important factor focused on in our research. The sliding model control used in [
14,
15] that demands the system to meet a relatively logical relationship between the mechanical torque (being a ‘sliding surface’) and the actual electrical power, is independent of the mathematical information about the studied system. Hence, sliding model control, applied for the integrated power control, maintains strong robustness. However, similar to the P&O method, the sliding model control also just describes the movement of steady operating points of the wind generator; consequently, the dynamic process of electrical power respecting the change of mechanical torque still needs to be avoided. At the same time, the determination of parameters of sliding model control requires experienced designers. In [
16], the authors selected Tip Speed Ratio (TSR) as the feedback parameter of the P&O method, and then compare the actual value of TSR with the ideal value calculated by mathematical model of studied system. Nevertheless, even it used the principle of P&O, and the method still performs with weak robustness. Different from the achievement discussed above, the research objective of the present work focused on the more general and flexible limited power demands, which can be applied in power balancing of a microgrid [
5,
10,
11], when the microgrid may include the small scale wind generator.
This paper presents the modelling of a small power wind PMSM in order to validate the power control strategy methods with hysteresis control loop. Proposed power control methods are designed to cover MPPT and PLC operating cases. In addition, this study faces precisely the problem of the uncertainty of wind velocity and the demanded power amount from load. Therefore, regarding the robustness of the studied system, it should be considered beside the main focus which is the wind speed. One notes that, in this paper, the imposed wind reference is modeled on a real wind measurement with many variations in frequencies and amplitudes. The small power wind turbine is emulated by a test bench and several experiments are implemented to validate characteristics of all proposed methods. Finally, experimental results are given, compared, and analyzed, and strengths and weaknesses of each method are revealed together.
The article is structured as follows.
Section 2 presents the small power conversion system including the analysis of characteristics. The formulation of the research problem and proposed power control methods integrating MPPT and PLC operating cases are presented in
Section 3. In
Section 4, the capability and effectiveness of all methods are evaluated based on a test bench. Conclusions and further studies are given in
Section 5 and the final section presents a nomenclature.
4. Analysis of Comparative Results
In order to compare above-mentioned power control methods, a real wind velocity is considered as the wind velocity input, presented in
Figure 11a, from data measured by Météo France, in Compiegne, France, on 15 January 2015, during 15 min; this real wind velocity profile is the same as in [
18]. Furthermore, the
profile was chosen based on the potential maximum power and the physical minimum power of the test bench, as presented in
Figure 11b. The selected wind profile and power limited profile highlight a strained condition with rapid changes.
Under these experimental conditions, several experimental tests are introduced to compare all above-mentioned power control methods whose characteristics are given as follow:
Fixed step-size: step-size equals 10 V, 7 V, 5 V and 2.5 V.
Improved variable step-size designed with Newton–Raphson technique: maximum value of step-size equals 10 V, 7 V, 5 V and 2.5 V.
Variable step-size based on fuzzy logic: the combination of parameters (K1, K2, Ks) respectively equal: (4.5, 17.5, 7), (4.5, 17.5 10), (5, 15, 7), (5, 15, 10), (5, 20, 7), (5, 20, 10), (10, 20, 7), and (10, 20, 10).
As key variable,
is used to analyze characteristics of each method. Referencing statistical concepts, the ‘mean’, defined as average value, and the ‘variance’, indicating the expected value of the squared deviation from the mean, are calculated to compare dynamic and steady-state characteristics of different power control methods. At first, to all methods based on the P&O theory, a sampling method is a sampling time equals two seconds, is applied to filter the peak of each perturbation step of P&O (marked as ‘Mean sampling’ and ‘Variance sampling’). Then, the overall comparison (marked as ‘Mean overall’ and ‘Variance overall’) is calculated and analyzed also. Based on those parameters, results for the optimal one test of each kind of method are collected and presented in
Figure 12. The ‘Mean’ and ‘Variance’ of those selected tests are listed in
Table 5.
Summarizing all presented results, under complex conditions of wind velocity and power demands variation, all three methods based on the P&O principle matched the design target of this integrating power control method. Those methods perform weakly in the view of dynamic, resulting from the mechanical inertia which cannot be ignored; but, overall, their steady-state errors are tiny. From fixed step-size to improved Newton–Raphson method calculating variable step-size till to fuzzy logic method, the dynamic noise is reduced significantly, meanwhile the change of whole steady-state error is not much, in the ‘overall’ view.
Considering the complexity of implementing each power control method, fixed step-size and improved Newton–Raphson method has just one parameter needing to be determined: the value or the maximum limit of step-size. In theory, variable step-size calculated by fuzzy logic has a greater possibility to perform better, since it contains several parameters to be modified. However, this greater freedom increases the complexity of determination of those parameters, which demands a rich experience of application.
5. Conclusions
Three power control methods based on the P&O principle (fixed step-size; improved Newton–Raphson variable step-size and variable step-size based on fuzzy logic) have been studied, designed, and then implemented into a test bench highlighting the sluggish mechanical inertia and dealing with the power control problem integrating MPPT and PLC cases. This study concerns the small power wind energy conversion system.
One experiment, based on designed wind and power demand profile, was used to validate the basic function of each method. In addition, another experiment, using a measured wind velocity profile and one calculated power demand profile, was implemented to compare characteristics of all proposed methods. Evaluations of all methods and several statistical indices of key variable were calculated and analyzed. All power control methods present good steady-state characteristics, but their dynamic characteristics are limited by the sluggish mechanical inertia and the control loop’s capability. Furthermore, some of the complex control algorithms, such as fuzzy logic used in this work, have the potential to achieve better performance. Moreover, the studied system uses a PMSM assembly, three-phase diode bridge, and converter with a hysteresis control, which makes it one of the most robust “drivers”.
The future research direction is to improve the dynamic characteristics of the control loop, to suppress the effect from the sluggish mechanical inertia. In addition, a deep robustness analysis may be conducted taking into account unmodeled dynamics, or associated couplings and uncertainties. This can significantly improve the performance of methods based on the P&O principle.