3.1.2. Estimation of the Annual Sales

If the electric tariff is known, then it is possible to estimate the annual sales (AS) attained from a TEP, which are directly related to knowing the annual energy produced (AEP) by the TEF. One of the most important indicators employed to discover whether it will be possible to commercially exploit a particular project is the estimation of the AEP, which usually depends on: (i) the information concerning the site; (ii) the devices used in the TEF; (iii) the energy export system; (iv) the characteristics of the current; (v) the ability of the device to capture energy; and (vi) the ability to convert and export the energy. The procedure employed to accurately estimate the AEP is shown in Figure 13, while the following expressions are required to compute the AEP for a TEF. A detailed description of the procedure developed (based on actuator disk theory) can be found in [46]:

$$\begin{aligned} V\_r &= V\_h \cdot \left(\frac{Z\_r}{Z\_h}\right)^{\frac{1}{2}}, \\ a &= 1 - \sqrt{1 - c\_{l\text{i}}}, \quad A\_s = \left(\frac{1 - 0.5a}{1 - a}\right) \cdot A\_{r\text{i}}, \quad V\_s = (1 - a) \cdot V\_{r\text{i}}, \\ A\_s \cdot V\_s^2 &+ (A\_l - A\_{r\text{i}}) \cdot V\_r^2 = A\_l \cdot V\_{z\text{i}}^2, \\ V\_x &= (V\_s - V\_z) \cdot e^{-0.2} \vec{\mathcal{H}}, \\ AEP &= \sum\_{i=1}^{\text{N}\_{\text{Uav}}} \sum\_{j=1}^{\text{N}\_{\text{Uav}}} P(i, j), \text{ where } P(i, j) &= \frac{1}{2} \cdot \mathbb{C}\_P \cdot \rho \cdot A\_r \cdot V\_x^3(i, j) \cdot \eta\_{PTO} \cdot \eta\_{AF} \cdot \eta\_{PS}, \\ AS &= p\_{ET} \cdot AEP, \end{aligned} \tag{2}$$

where *Vr* symbolizes the velocity of the rotor, *Vh* expresses the velocity on the sea surface, *Zr* denotes the depth of the rotor, *Zh* represents the water column depth, *a* symbolizes the axial induction factor, *ct* denotes the thrust coefficient, *Vr* represents the free stream velocity at the rotor depth, *Ar* is the surface of the rotor, *Vs* denotes the flow velocity at the rotor of the turbine, *As* represents the output flow surface, *At* symbolizes the total frontal surface of the TEC, *Vz* expresses the final velocity of the blended flow, *D* denotes the diameter of the rotor, (*x*, *Vx*) represents an intermediate point located between the rotor output and the blend flow downstream, *Nrow* and *Ncolumn* are, respectively, the number of rows and columns on the farm, *CP* denotes the power coefficient, *P*(*i*, *j*) denotes the power of the TEC located in row *i* and column *j* on the farm, *ρ* symbolizes the fluid density, *ηPTO* is the performance of the power take off (PTO), *ηAF* denotes the availability factor, *ηPES* represents the performance of the power export system and, finally, *pET* is the electric tariff.

**Figure 13.** How annual sales are computed: A summary.
