**3.1. Hydraulic machine**

We start from the conversion of the kinetic energy of the water into mechanical rotational energy of the hydraulic machine runner. Different typologies of machine are considered for the hydraulic machine: water turbines for mini and micro power plant and a gear pump. The water turbines for micro-hydropower generation can be classified into two main categories: impulse turbines and reaction turbines as described in (Inversin 1994) and listed in Fig. 2. In impulse turbines there is no expansion of the flow within the moving blades of the runner and, as such, the pressure remains constant while passing over the blades. In reaction turbines the stream expands as it flows over the blades, therefore producing a drop in pressure which gives a reaction and hence motion to the rotor.

**Figure 2.** Classification of turbines for micro-hydropower generation

In general, impulse turbines are used for high head plants while reaction turbines for low head sites.

470 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

the rotating parts.

**Table 2.** Design choices

mutual interactions.

**3.1. Hydraulic machine** 

**3. Trade off and design** 

with the precision that can be reached with standard production process of some details of the generator unit as impeller and bushings. A limited angular speed also ensures an adequate degree of durability and strength. This speed value is precautionary as regards the possibility of creating vibrations, that may occur at higher speeds and lead to the failure of

**Parameter Symbol Value Unit** 

This phase is carried on by splitting the system in its three subsystems. Following the transformations of energy that take place in the device the hydraulic machine is met first, then the electric machine and finally the energy storage unit, without neglecting their

We start from the conversion of the kinetic energy of the water into mechanical rotational energy of the hydraulic machine runner. Different typologies of machine are considered for the hydraulic machine: water turbines for mini and micro power plant and a gear pump. The water turbines for micro-hydropower generation can be classified into two main categories: impulse turbines and reaction turbines as described in (Inversin 1994) and listed in Fig. 2. In impulse turbines there is no expansion of the flow within the moving blades of the runner and, as such, the pressure remains constant while passing over the blades. In reaction turbines the stream expands as it flows over the blades, therefore producing a drop

in pressure which gives a reaction and hence motion to the rotor.

**Figure 2.** Classification of turbines for micro-hydropower generation

inlet nozzle diameter *d* >4 mm generator rated speed *n* 1000 rpm The turbines available on the market are usually very large compared to what needed for the present application, so a new turbine needs to be designed following the indications and design criteria of classical hydropower turbines of much larger dimensions.

For a given nominal output rated power and flow rate, equation (1) allows evaluating the pressure drop across the hydraulic machine:

$$P\_n = \mathbb{Q} \cdot \Delta p \tag{1}$$

Then, from the energy conservation principle of an ideal fluid inside a pipeline (i.e. the Bernoulli's principle) it is possible to determine the head of the water flow *H*.

$$
\Delta p \text{=} \rho \cdot \text{g} \cdot \text{H} \tag{2}
$$

From the head *H*, the absolute mean speed c of the water jet at the nozzle output can be found following the classical design indications of a Pelton turbine:

$$\mathfrak{c} \circ \mathfrak{p} \cdot \sqrt{2 \cdot \mathfrak{g} \cdot H} \tag{3}$$

where *ϕ* is the nozzle flow factor, evaluated in the present case as equal to *0.97*. As reported in (Nechleba, 1957), the best efficiency is reached when the circumferential speed of the runner (also indicated as drag speed) is related to the water jet speed as follows:

$$
\mu = 0.46 \cdot \text{c} \tag{4}
$$

The circumferential speed *u* can then be related to the diameter *A* of the rotor and to the angular speed *n* of the runner:

$$A = \frac{60 \cdot u}{\pi \cdot n} \tag{5}$$

where *u* is expressed in meter per second and *n* in revolutions per minute.

A trade-off analysis has been performed between different kind of turbines by making the preliminary design of the runner. The case of hydraulic gear motor has been included in the trade off study along with the classical Francis, Pelton, and Banki turbines . The results of the preliminary design are presented in Tab. 3. All of them are compatible in size with the design specifications.

In addition to the preliminary design, other critical aspects related both to functionality and practical feasibility have been considered in the trade-off. In particular, the overall dimensions of the different layouts have been evaluated along with the possibility to integrate the rotor of the electric machine to that of the turbine, and with the need of avoiding chocking due to the debris transported by the water flow. Finally, the constructive complexity of the different parts has also been considered, in particular focusing on rotor

and stator. Each of these aspects have been ranked in a three step scale. The results of this trade-off are reported in Tab. 4.


**Table 3.** Preliminary design of hydraulic machines. Comparison of the main parameters of the different solutions.


\*\*\* good, \*\* average, \* bad

**Table 4.** Trade-off analysis between hydraulic machines.

### *3.1.1. Cross Flow or Banki turbine design*

The Cross Flow or Banki turbine appears to be the best in almost all aspects examined. Its strengths are the simplicity of construction, the compact size, a good interfacing capability with the generator and a limited risk of choking.

Following the Banki water turbine theory reported in (Mockmore et al. 1959) the two main parts of the turbine, namely the nozzle and the runner, have been designed. The design drawings of the Banki turbine runner are shown in Fig. 3, and its characteristic parameters are given in Tab. 5.

**Figure 3.** Banki turbine runner: a) 3D model. b) geometrical parameters.


**Table 5.** Cross flow or Banki turbine construction parameters.
