*Article* **Conceptual Study of Vernier Generator and Rectifier Association for Low Power Wind Energy Systems**

**Philippe Enrici 1,\*, Ivan Meny 2 and Daniel Matt 1**


**Abstract:** In this paper, we study a wind energy conversion system designed for domestic use in urban or agricultural areas. We first present the turbine, which was specifically designed to be installed on the buildings that it supplies. Based on turbine characteristics, we perform analytical sizing of a Permanent Magnet Vernier Machine (PMVM), which will be used as a generator in our energy conversion system. We show the influence of this generator on system operation by studying its association with a PWM rectifier and with a diode bridge rectifier. We then seek to improve generator design so that the turbine operates closely to maximum power points, while using a simple and robust energy conversion system. We use simulation to show the improvements achieved by taking into account the entire energy conversion system during machine design.

**Keywords:** converter–machine association; direct drive machine; Permanent Magnet Vernier Machine; synchronous generator; wind energy system for domestic applications; renewable energy

**1. Introduction**

> Concurrently with the increasing existence of wind farms offering power of several megawatts [1], the expansion of small wind turbines can also be observed, with power ranges from 1 to 50 kW [2–4]. When associated with other energy sources, these turbines can provide a self-sufficient supply of power for a home or remote location. As such, they avoid costly, or even impractical, connections to the grid, which can actually be a significant source of energy loss with regard to the power transmitted over the line.

> In electrical installations already connected to the grid, small turbines help reduce the relatively low efficiency of centralized production, while increasing the share of renewable energies in electric power production. In addition, their smaller footprints, and the fact that they are not grouped in wind farms, reduce visual impact, which is one of the greatest reasons for opposing the development of this energy source. However, if the risk of nuisance is rather low in rural areas, turbines must be designed specifically for use in urban areas, so as to be both acoustically and visually discreet.

> In this article, we study the entire energy conversion system associated with a wind turbine designed specifically for use in urban areas. This system includes a Vernier machine, which is considered as a suitable alternative for direct-drive applications. The performance of this machine has already been the subject of several studies, but its integration in an electromechanical conversion system has not been investigated thoroughly. Our objective in this paper is to design a Vernier machine to extract a maximum amount of energy from the turbine by implementing a simple and robust energy conversion system. To reach this goal, we are particularly interested in the association of the Vernier machine with a diode bridge rectifier.

**Citation:** Enrici, P.; Meny, I.; Matt, D. Conceptual Study of Vernier Generator and Rectifier Association for Low Power Wind Energy Systems. *Energies* **2021**, *14*, 666. https:// doi.org/10.3390/en14030666

Academic Editor: Adolfo Dannier Received: 14 December 2020 Accepted: 25 January 2021 Published: 28 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **2. The Vertical Axis Wind Turbine**

In order to meet market requirements for small wind turbines designed to be used in urban areas, the Gual Industrie Company has developed a vertical axis turbine [5], the StatoEolian, shown in Figure 1. This wind turbine is located in Occitanie region in the south of France. This turbine is comprised of an external stator surrounding a paddle rotor. The stator channels the wind at its optimal force onto the rotor. Performance improvement requires a thorough study of the interactions between the different geometric parameters of the turbine. An important quality of this device is that it even remains operational in severe storms.

**Figure 1.** (**a**) The vertical axis turbine installed on a house; (**b**) the wind turbine.

#### *2.1. Characterization of the Turbine*

A measurement campaign over several weeks made by the laboratory enabled us to model the aerodynamic torque *TT* (in Nm) developed by the turbine as a function of wind speed *Sw* (in m/s), and of rotation speed *NT* (in rpm):

$$T\_T = 1.5 \cdot S\_W^2 - 0.275 \cdot N\_T \cdot S\_W \tag{1}$$

This model was used to deduce torque/speed (Figure 2) and power/speed (Figure 3) characteristics for wind speeds ranging from 6 m/s to 22 m/s.

**Figure 2.** Turbine torque for wind speeds ranging from 6 m/s to 22 m/s.

**Figure 3.** Turbine power for wind speeds ranging from 6 m/s to 25 m/s.

Unlike horizontal axis turbines, the torque value is particularly high when the turbine starts, and it decreases when the rotation speed rises. A more classical bell-shaped curve is observed for power characteristic. One of the main purposes of the energy conversion system, associated with the turbine, will therefore be to keep its working point as close as possible to the maximum power points (dotted curve in Figure 3).

#### *2.2. Generator for the Middle Wind Turbine Characterization of the Turbine*

The gearbox is a significant cause of breakdown in a wind turbine, and therefore requires maintenance operations to prevent or correct these failures. This last point is particularly problematic in the case of domestic installations, where users are not likely to possess the skills needed for repairs. The installation could thus be out-of-order for a relatively long time, particularly in a remote area.

The entire energy conversion system must be sturdy. It can face extreme conditions, such as violent winds, possibly without any people being present to perform a safety shutdown. To meet these constraints, and to ensure operation of the turbine without failure for as long as possible, the gearbox is generally oversized in domestic wind turbines. As a result, the gearbox price rises and its integration into the wind energy system becomes more difficult. Another solution is to eliminate the gearbox by using a direct-drive generator.

To make a generator with a high torque-to-weight ratio, essential for implementing a direct-drive, we propose to use a Surface Permanent Magnet Vernier Machine (SPMVM). In this machine, the high torque feature is brought about by the so-called "magnetic gearing effect": a small movement of the rotor induces a large change in flux, which results in high torque.

By taking into account the high value of mean wind speeds recorded at the turbine installation site, as well as the dimensioning variables of the generator, we calculated its rated values for a wind speed of 19 m/s.

The choice of this wind speed was made based on the wind speed readings at the site where the vertical axis wind turbine is installed. This location is one of the windiest French regions with 300 to 350 days of wind per year. The wind is gusty, with large wind variations and up to maximum wind speeds of 24 m/s. The energetic study allowed the determination of the most interesting peak wind speed for the dimensioning. The choice of this wind speed could have been lower but the aim was also in the case of this turbine to show its ability to operate under high wind speeds. For other sites the choice of this peak speed must be predetermined.

We thus obtained:


#### **3. The Permanent Magnet Vernier Machine**

#### *3.1. Principle of Permanent Magnet Vernier Machine*

The Permanent Magnet Vernier Machine (PMVM) is an interesting alternative to a conventional Permanent Magnet Synchronous Machine (PMSM). It is less well known despite being the subject of many studies [6–10].

PMVMs allow attainment of high mass torques of interest to obtain direct drive generators suitable for low-speed vertical axis turbines used in proximity to wind turbines. They are also efficient for horizontal axis wind turbines compared to synchronous machines with a large number of poles. The PMVMs have sinusoidal electromotive force (e.m.f.) and the torque ripple is almost zero.

The manufacturing cost and reliability of a PMVM is identical to that of a conventional synchronous machine. The objective of the rest of the article is to show the interest of associating a PMVM with a diode rectifier whose association has been optimized. Thus, the economic cost and reliability of the unit are interesting for an urban or rural environment for small powers.

The Permanent Magnet Vernier Machine we present in this article (PMVM) is an evolution of the Vernier Reluctance Machine (VRM).

The polar coupling in a permanent magne<sup>t</sup> machine is defined when the fundamental interaction of currents and magnets takes place at the pole pitch level, which is the repeating pattern of the stator winding. The toothed coupling is defined when the fundamental interaction of currents and magnets takes place at the tooth pitch scale, which is the length between two slots. When the winding is distributed, the actuator has two forms of coupling: a toothed type and a polar type. This machine is also called a Vernier effect machine [11].

As shown in Figure 4, the rotor teeth row of the VRM has been replaced by an alternate magnets row to obtain the VRMM.

**Figure 4.** Principle of the Permanent Magnet Vernier Machine.

In a motor, the torque is produced by the interaction of stator and rotor magnetic fields. For its two machines the winding is identical, we have a polyphase winding with pairs of p poles distributed with NS number of slots.

In the PMVM, the tooth pitch is nearly equal to mechanical pitch, defined as the angle covered during an electric period. The number of rotor magne<sup>t</sup> pairs *NR* is different from the number of stator teeth *NS*. The condition to be met is:

$$|N\_S - N\_R| = p \tag{2}$$

Moreover, the electrical frequency f of the PMVM is uniquely linked to the number of pairs of magnets *NR*, as seen in the following formula:

$$f = \frac{1}{T} = \frac{N\_R \cdot \Omega\_R}{2\pi} \tag{3}$$

with Ω*R* is the rotor speed in rd/s.

The PMVM is a tooth coupling machine. However, the study of this type of machine is identical to that of a conventional synchronous machine. From the Maxwell tensor we can write for the expression of the torque:

$$T\_{\rm cm} = K\_V \cdot R\_c^{-2} \cdot L \cdot \int\limits\_{2\pi} b\_{1\text{on}} \cdot \lambda\_1 \cdot d\Theta \tag{4}$$

The dimensions *Re* and *L* of expression (4) represent the air gap radius and iron length. The coefficient *Kv*, the speed ratio, is called the Vernier Ratio. This coefficient is difference between the stator field speed and the rotor speed. The stator field speed Ω*S* is:

$$
\Omega\_{\mathbb{S}} = \frac{w}{p} \tag{5}
$$

The rotor speed Ω*R* is:

$$
\Omega\_R = \frac{\omega}{N\_R} \tag{6}
$$

We obtain:

$$\frac{\Omega\_S}{\Omega\_R} = K\_V = \frac{N\_R}{P} \tag{7}$$

We use for our study the linear density of current, λ1, equivalent to stator winding. The periodicity for λ1 is equal to <sup>2</sup>π/*p*, which we express as:

$$
\lambda\_1 = A\_1 \cdot \cos(p \cdot \theta) \tag{8}
$$

The amplitude *A*1 of the linear density depends on the current in the slot, the winding coefficient and the shape of the slot. The stator air gap permeance has equal to 2π/*NS*.

The air gap magnetomotive force created by the magne<sup>t</sup> has a periodicity equal to 2π/|*NS* − *NR*|. The fundamental field component *b*1*an* can be expressed as follows:

$$b\_{1an} = k\_1 \cdot M \cdot \cos((N\_S - N\_R) \cdot \theta) \tag{9}$$

with *M* as the Remanent flux density of magnet. The coefficient *k*1, which defines the field amplitude *b*1*an*(θ), is deduced using the finite element [10]. Its value, which depends on the ratios of the dimensional proportion parameters, is generally between 0.1 and 0.2.

In the PMVM, the increase in operating frequency allows a gain on the mass–power ratio at very low speed compared to a PMSM.

#### *3.2. Example of Permanent Magnet Vernier Machine Prototype*

The Figure 5 shows an example of a prototype designed to simulate a Vernier effect generator for an energy conversion system.

This prototype has the following characteristics:


**Figure 5.** (**a**) Stator of the Vernier machine; (**b**) rotor of the Vernier machine.

A particularity of the Vernier machine is that its fem is sinusoidal. There is an e.m.f. of the prototype on Figure 6.

**Figure 6.** Electromotive force (e.m.f.) induction of Vernier machine at 1000 rpm and f = 367 Hz.

## **4. Sizing of Generator**
