**1. Introduction**

In recent years, the evolution of renewable energy sources such as solar, hydroelectric, wind energy, biogas and geothermal energies have gained global attention. Rahim et al. [1] reported that an isolated self-stand generating strategy is desired to achieve electrification in distant areas. The conventional stand-alone energy generation system utilizes a synchronous generator that requires a direct current field excitation. Nagria et al. [2] identified that the convectional energy generating methods are not suitable for rural electrification. Instead, a self-stand and self-excited generating system will be more convenient for such applications, as depicted in **Figure 1(b)**. For machines like synchronous reluctance machines and induction machine, selfexcitation can be realized by the interconnection of excitation capacitors in star or delta across the stator end terminals, allowing them to be used as a self-stand generator [3–5]. In self excited induction generator, SEIG offers certain merits over a synchronous generator (convectional) as a source of separated to supply electric power, such as rugged structure, reduced size, low cost, low maintenance requirements and lack of DC source for excitation [5–7]. In spite of that, in SEIG the generated voltage frequency is influced by the loads and the capacitor bank. A self-excited or self-stand synchronous reluctance generator (SRG) has almost all the advantages of a

**(b)**

#### **Figure 1.**

*(a) Dq axes reference frame of the SRG. (b) Power generating system.*

self-excited induction generator. In addition, its rotor copper losses and the output frequency are not much influenced by the load, i.e., the load variations do not significantly affect the rotor speed and frequency of output voltage [8, 9].

In literature, only few mathematical models have been built to determine the performance of a self-excited synchronous reluctance generator. Abdel-Kader et al. [10] attempted to develop an equivalent circuit for the SRG in the same manner as the SEIG. Yawei Wang et al. [5] also attempted analysis and modeling of self-excited synchronous reluctance generators. But, the load is limited to no load and resistive load conditions. Moreover, the effects of core losses and saturation effects are neglected, although the losses and saturation have significant effect on the performance of the machine. Rahim H. et al. [11–14], investigated dq axes transformation based model and demonstrated its validity. T. F. Chan. et al. [12], develops a two-axis theory to model and analyze a three-phase self-excited reluctance generator which supplies to an isolated inductive load. However, in this survey, simple method to estimate the excitation capacitor is not included. Nevertheless, these research papers

*Wind Turbine and Synchronous Reluctance Modeling for Wind Energy Application DOI: http://dx.doi.org/10.5772/intechopen.103775*

are mostly based on conventional salient rotor synchronous reluctance generators, i.e., no magnetic material or bridges in the rotor.

In this Chapter, wind turbine modeling, design and an analytical model in the dq rotor reference frame is developed as shown in **Figure 1(a)**. In addition, the resistive load is considered to estimate the performance of the SRG. A new and simple method to estimate the minimum capacitance requirement for the resistive load is applied.

### **2. Wind turbine model**

Among renewable energy sources in the world, the wind energy is more environmental and economical to generate electricity. In recent days, there is remarkable expansion in the use of wind energy generation. This result in the importance in developing in turbine and generators of maga power rating. For this reason the recent work is more based on the development of high efficiency, and low cost generators for remote area applications. The rating of the turbine is in the range of kilo watt. The turbine performance coefficient in terms of blade pitch angle and tip speed ratio (TSR) is given in Eq. (1) [15]:

$$\mathbf{C}\_{p}(\lambda, a) = \mathbf{C}\_{1} \left( \frac{\mathbf{C}\_{2}}{\lambda\_{1}} - \mathbf{C}\_{3}a - \mathbf{C}\_{4} \right) \exp \frac{-\mathbf{C}\_{5}}{\lambda\_{1}} + \mathbf{C}\_{6}\lambda \tag{1}$$

Letting,

$$\lambda\_1 = \frac{(a^3 + 1)(\lambda + 0.08\alpha)}{a^3 - 0.028a - 0.035\lambda + 1} \tag{2}$$

For various types of wind turbine, the values of C1 � C6 are different. **Figure 2** depicts the group power coefficient curves and tip speed ratio for C1, C2, C3, C4, C5 and C6 as 0.200, 119, 0.4, 5.5, 12.5, and 0, respectively. The turbine output power is given in (watts)

*Pm* <sup>¼</sup> <sup>1</sup> 2 *R*3 *πρaCp*ð Þ *<sup>λ</sup>*, *<sup>α</sup>* V3 *<sup>w</sup>* (3)

**Figure 2.** *Performance coefficient at pitch angle α = 0.*

The value of λ has been selected for optimal point of Cp at α = 0 as shown in **Figure 2**. Once the values of λ and Cp are found, the turbine speed and the radius are calculated from (3) and (4). The tip speed ratio can be determine from:

$$
\mathbf{Q} = \lambda \mathbf{v}\_{\mathbf{v}} /\_{\mathbf{R}} \tag{4}
$$

The torque causing the rotation of the wind turbine shafts depends on the turbine rated power output and angular velocity. It can be expressed as:

$$T\_m = {}^{P\_m}\!/\Omega = \frac{1}{2\lambda} \text{R}^4 \pi \rho\_a \text{C}\_p(\lambda, a) \text{V}\_w^2 \tag{5}$$

The gearbox is utilized to transfer torque to the generator shaft rotating at a higher speed in the wind turbine. The wind turbine side to generator side gear ratio can be expressed as:

$$R\_G = \% \Omega \tag{6}$$

Here, Ω and ω are the turbine and rotational speed of the generator, respectively. Eqs. (1) to (6) are used to design a wind turbine that can produce an output shaft power of 1 kW at a rated mean wind speed of 8 meter per second.

The designed parameters of the wind turbine is summarized in **Table 1**. The variation of power coefficient of the wind turbine for different blade pitch angle α is shown in **Figure 2**. **Figure 3**, shows the generated mechanical power at different wind velocity. From **Figure 3**, it is observed that as the wind speed increases, the rotational speed of the turbine also needs to be increased to extract maximum power out of the turbine. It is also observed that for the designed wind turbine, the maximum power attains near 32 rad/s for the average wind speed of 8 m/s.

**Figure 4**, shows the torque causes mechanical rotation at different wind velocity. From **Figure 4**, it can be observed that as the wind speed increases, the rotational speed of the turbine also needs to be increased to extract maximum rotational torque of the turbine.


#### **Table 1.**

*Initial data and calculated values of the wind turbine parameters.*

*Wind Turbine and Synchronous Reluctance Modeling for Wind Energy Application DOI: http://dx.doi.org/10.5772/intechopen.103775*

**Figure 3.** *Turbine power characteristics at pitch angle α = 0.*

**Figure 4.** *Turbine torque characteristics at pitch angle α = 0.*
