Use of the Dual Stator Induction Machine in Photovoltaic - Wind Hybrid Pumping

Use of the Dual Stator Induction Machine in Photovoltaic - Wind Hybrid Pumping

Arezki AdjatiToufik Rekioua Djamila Rekioua 

Laboratoire de Technologie Industrielle et de l’Information, Faculté de Technologie, Université de Bejaia, Bejaia 06000, Algeria

Corresponding Author Email: 
adjati@hotmail.fr
Page: 
115-124
|
DOI: 
https://doi.org/10.18280/jesa.540113
Received: 
17 August 2020
|
Revised: 
14 December 2020
|
Accepted: 
20 December 2020
|
Available online: 
28 February 2021
| Citation

© 2021 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).

OPEN ACCESS

Abstract: 

In this article, a combination of two renewable sources is used to power a pumping station. Indeed, a photovoltaic generator (GPV) and a wind turbine are installed so as to be complementary in the process of filling the water tower similar to an accumulator, before distributing the water by gravity. Prior knowledge of a few quantities, in particular the assessment of water requirements, total dynamic head (TDH) and flow rate is essential for sizing the various components of the pumping chain. The results obtained show that the combination of the energy of the sun with that of the wind ensures a continuity of service; the use of an engine (DSIM) and a double stator induction generator (DSIG) allows degraded mode operation in the event that one or more parts of the drive system are defective. The global system is dimensioned and simulated under Matlab/ Simulink Package.

Keywords: 

centrifugal pump, dual stator induction motor (DSIM), dual stator induction generator (DSIG), hybrid pumping system (HPS), photovoltaic generator (GPV), renewable energy, wind turbine

1. Introduction

In full swing, the real bet of the industrialized countries is, without doubt, the search for new sources of energy, preferably renewable, in substitution for the usual so-called conventional sources. A combination of the two available and inexhaustible energies, including the energy of the sun and that of the wind, will be an excellent alternative to electrify isolated sites not connected to electrical networks and supply pumping stations to draw water [1].

Semmache et al. [2] had opted for a combination of solar and conventional energy in order to reduce the consumption bill and preserve the environment by using so-called green energies. To obtain better control and better optimization between the different functions of the elements of a photovoltaic pumping system Mayssa and Sbita [3] have inserted an intelligent control method to provide the maximum power point with an improvement in system performance by obtaining a pumping flow of up to three times more.

Khan et al. [4] found that irrigation with solar power of certain crops like potato, cotton, soy, sunflower, strawberry, lentil, mustard are very much lucrative compared to diesel powered irrigation.

Hajdidj et al. [5] had introduced a battery storage system to the PV-wind hybrid system and had identified the main obstacle to energy production for hybrid systems, which is only the failure of one of the sources.

For our part, we opted for a double stator induction motor (DSIM) to drive the centrifugal pump and we used the double stator induction generator (DSIG) for the wind turbine. The reason for this convincing choice is undoubtedly the increased reliability and robustness of the double star induction machine that can still rotate even in the event of loss of supply phases or short circuit in the stator windings and provide the torque necessary to pump water under degraded conditions [6].

Besides to the fact that hybrid pumping makes it possible to obtain clearly significant flow rates, our proposal to combine these two renewable energies is justified by the fact that photovoltaic (PV) and wind turbine are not in competition, but on the contrary, they can strengthen mutually, while saving the additional cost of batteries which are simply replaced by a large capacity water tower.

2. Components of Hybrid Pumping System

As shown in Figure 1, this system consists of a photovoltaic source and a wind turbine equipped with a DSIG, an AC/DC converter, two DC/DC converters, two DC/AC inverters which supply the DSIM which drives a centrifugal pump which draws water from a borehole towards a water tower in order to distribute it by gravity [6, 7].

Figure 1. Hybrid photovoltaic-wind turbine installation

2.1 DSIM model

The power segmentation of multiphase machines is obtained when the number of phases of the stator increases, which leads to a decrease in the current per phase without the voltage per phase being increased. The total power is thus distributed over the different phases [8].

The electrical equations of the DSIM are given as [8]:

$\left[\begin{array}{c}v_{a 1} \\ v_{b 1} \\ v_{c 1}\end{array}\right]=\left[\begin{array}{ccc}R_{s} & 0 & 0 \\ 0 & R_{s} & 0 \\ 0 & 0 & R_{s}\end{array}\right]\left[\begin{array}{c}i_{a 1} \\ i_{b 1} \\ i_{c 1}\end{array}\right]+\frac{d}{d t}\left[\begin{array}{c}\varphi_{a 1} \\ \varphi_{b 1} \\ \varphi_{c 1}\end{array}\right]$

$\left[\begin{array}{c}v_{a 2} \\ v_{b 2} \\ v_{c 2}\end{array}\right]=\left[\begin{array}{ccc}R_{s} & 0 & 0 \\ 0 & R_{s} & 0 \\ 0 & 0 & R_{s}\end{array}\right]\left[\begin{array}{c}i_{a 2} \\ i_{b 2} \\ i_{c 2}\end{array}\right]+\frac{d}{d t}\left[\begin{array}{c}\varphi_{a 2} \\ \varphi_{b 2} \\ \varphi_{c 2}\end{array}\right]$

$\left[\begin{array}{c}0 \\ 0 \\ 0\end{array}\right]=\left[\begin{array}{ccc}R_{r} & 0 & 0 \\ 0 & R_{r} & 0 \\ 0 & 0 & R_{r}\end{array}\right]\left[\begin{array}{c}I_{a r} \\ I_{b r} \\ I_{c r}\end{array}\right]+\frac{d}{d t}\left[\begin{array}{c}\varphi_{a r} \\ \varphi_{b r} \\ \varphi_{c r}\end{array}\right]$      (1)

The magnetic equations are:

$\left[\begin{array}{l}\varphi_{1, a b c} \\ \varphi_{2, a b c} \\ \varphi_{r, a b c}\end{array}\right]=\left[\begin{array}{ccc}L_{s 1, s 1} & L_{s 1, s 2} & L_{s 1, r} \\ L_{s 2, s 1} & L_{s 2, s 2} & L_{s 2, r} \\ L_{r, s 1} & L_{r, s 2} & L_{r, r}\end{array}\right]\left[\begin{array}{l}i_{1, a b c} \\ i_{2, a b c} \\ i_{r, a b c}\end{array}\right]$    (2)

The magnetic energy is [9]:

$\omega_{m a g}=\frac{1}{2}\left(\left[I_{s 1}\right]^{t}\left[\phi_{s 1}\right]+\left[I_{s 2}\right]^{t}\left[\phi_{s 2}\right]+\left[I_{r}\right]^{t}\left[\phi_{r}\right]\right)$    (3)

The electromagnetic torque is given by the derivative of magnetic energy versus mechanical angle [8, 9].  

$T_{e m}=\frac{d \omega_{m a g}}{d \theta_{m}}=p \cdot \frac{d \omega_{m a g}}{d \theta_{e}}$    (4)

The basic mechanical equation that governs the movement of the rotor of the DSIM can be given by [6]:

$I . \frac{d \Omega}{d t}=T_{e m}-T_{r}-F_{r} . \Omega$    (5)

Reliability is ensured by operation under degraded conditions and spatial harmonics of a certain order are eliminated. Torque ripples are damped faster in a multi-phase machine and the power factor is improved compared to the three-phase asynchronous machine [10].

The use of a voltage inverter unfortunately causes current harmonics of large amplitude and the fact that the number of phases is large, the number of semiconductors used also increases, which generates an additional cost of the installation [10, 11].

2.2 GPV modeling

The explicit Rauschenbach model offers equations which allow the characteristic curve of a solar cell to be generated by knowing the open circuit voltage "Voc", the maximum power voltage "Vm", the short-circuit current "Icc" and the current at maximum power "Im" [12].

Figure 2 represents the GPV which generates the following current:

$I=I_{c c} \times\left[1-C_{1} \times\left[\exp \left(\frac{V}{V_{o c} \times C_{2}}-1\right)\right]\right]$    (6)

Figure 2. Diagram of photovoltaic generator

The constants C1 and C2 are defined by:

$C_{1}=\left(1-\frac{I_{m}}{I_{c c}}\right) \times \exp \left(\frac{-V_{m}}{V_{o c} \times C_{2}}\right)$

$C_{2}=\left(\frac{V_{m}}{V_{o c}}-1\right) / \ln \left(1-\frac{I_{m}}{I_{c c}}\right)$    (7)

The voltage "Vm" corresponding to the maximum power is calculated by the equation [13]:

$V_{m}=V_{\text {meef }}\left[1+\Delta V_{m}\left(T_{j}-T_{\text {jief }}\right)\right]+K_{1} V_{T} \ln \left(\frac{G_{s}}{G_{\text {sref }}}\right)+K_{2} V_{T} \ln ^{2}\left(\frac{G_{s}}{G_{\text {sref }}}\right)$    (8)

The current "Im" corresponding to the maximum power is obtained by [13]:

$I_{m}=I_{m r e f} \times\left(\frac{G_{s}}{G_{s r e f}}\right) \times\left[1+\Delta I_{m} \times\left(T_{j}-T_{j r e f}\right)\right]$    (9)

where, Vmref, Imref: Voltage & current at maximum power point in standard condition, ΔVm, ΔIm: Temperature coefficient of voltage and current at the point of maximum power and α, β: Constant parameters.

For the levels of sunshine Gs [W/m²] and temperature T [℃], it is possible to use some equations in order to obtain new points from the reference points of sunshine and of the temperature [14].

$\left\{\begin{array}{c}\Delta I=\alpha \times\left(\frac{G_{s}}{G_{s r e f}}\right) \times \Delta T+\left(\frac{G_{s}}{G_{s r e f}}-1\right) \times I_{c c} \\ \Delta V=-\beta \times \Delta T-R_{s} \times \Delta I\end{array}\right.$    (10)

And the new values of current and voltage are:

$\left\{\begin{array}{l}I_{\text {new }}=I_{\text {ref }}+\Delta I \\ V_{\text {new }}=V_{\text {ref }}-\Delta V\end{array}\right.$    (11)

2.3 Turbine modeling

For deep wells with high flow rates, electric wind pumping is most suitable for isolated and fairly windy sites, with a competitive advantage compared to other energy sources. These isolated wind turbines are mainly used to supply residential areas or isolated telecommunication systems [15].

The electric system of a fixed-speed wind turbine is simpler and less expensive compared to variable-speed operation that offers increased energy efficiency and reduced torque oscillations. The majority of wind power applications are at constant speed, which allows the reactive energy of the self-priming capacitors to be controlled [15].

Figure 3. Electric pumping diagram

Figure 3 represent the electric pumping diagram and the aerodynamic power is given by:

$P_{e o l}=P_{T}=\frac{1}{2} \times \rho \times \pi \times R^{2} \times C_{p}(\lambda) \times V^{3}$    (12)

The turbine torque will therefore be:

$T_{T}=\frac{P_{T}}{\Omega_{T}}=\frac{1}{2} \times \rho \times \pi \times R^{3} \times C_{p}(\lambda) \times V^{2}$    (13)

where, ρ: air density, R: blade length and V: wind speed.

For a small power wind turbine, the analytical equation of Cp as a function of λ is given by [16]:

$C_{p}(\lambda)=7.9863 \times 10^{-5} \times \lambda^{5}-17.375 \times 10^{-4} \times \lambda^{4}$

$-9.86 \times 10^{-3} \times \lambda^{3}-9.41 \times 10^{-3} \times \lambda^{2}+6.38 \times 10^{-2} \times \lambda+0.001$          (14)

2.4 DSIG modeling

The expression of the magnetization current is given as a function of the direct and quadrature magnetization currents by [17, 18]:

$\mid \begin{array}{l}i_{m d}=-i_{d 1}-i_{d 2}+i_{d r} \\ i_{m q}=-i_{q 1}-i_{q 2}+i_{q r}\end{array} \rightarrow i_{m}=\sqrt{i_{m d}^{2}+i_{m q}^{2}}$    (15)

The DSIG is driven at a speed greater than that of synchronism and the self-priming of the generator is achieved through the addition of capacitors with precise values, added to this, the presence of a remanent field in the rotor iron [17].

The magnetizing inductance as a function of the magnetizing current “im” is given by [19, 20]:

$L_{m}=0.1406+0.0014 \times i_{m}-0.0012 \times i_{m}^{2}+5 \times 10^{-5} \times i_{m}^{3}$    (16)

The electromagnetic torque is given by:

$T_{e m}=\frac{3 \times p \times L_{m}}{2 \times\left(L_{r}+L_{m}\right)}\left[\varphi_{d r} \times\left(i_{q 1}+i_{q 2}\right)-\varphi_{q r} \times\left(i_{d 1}+i_{d 2}\right)\right]$    (17)

And the movement of the rotor can be governed by the following mechanical equation:

$T_{e m}=I \times \frac{d \Omega}{d t}+F_{r} \times \Omega+T_{r}$    (18)

The DSIG differential equation systems according to the "d, q" standard are given by the following electrical equations:

$\left\{\begin{array}{c}V_{d r}=r_{r} \times i_{d r}+p \times \varphi_{d r}-\left(\omega_{s}-\omega_{r}\right) \times \varphi_{q r}=0 \\ V_{q r}=r_{r} \times i_{q r}+p \times \varphi_{q r}+\left(\omega_{s}-\omega_{r}\right) \times \varphi_{d r}=0 \\ V_{d 1}=-r_{s} \times i_{d 1}+p \times \varphi_{d 1}-\omega_{s} \times \varphi_{q 1} \\ V_{q 1}=-r_{s} \times i_{q 1}+p \times \varphi_{q 1}+\omega_{s} \times \varphi_{d 1} \\ V_{d 2}=-r_{s} \times i_{d 2}+p \times \varphi_{d 2}-\omega_{s} \times \varphi_{q 2} \\ V_{q 2}=-r_{s} \times i_{q 2}+p \times \varphi_{q 2}+\omega_{s} \times \varphi_{d 2}\end{array}\right.$    (19)

The rotor and stator flux according to the “d, q” reference frame is given by [21]:

$\left\{\begin{array}{c}\left\{\begin{array}{l}\varphi_{d t}=L_{r} \times i_{d r}+L_{m d} \times i_{m d} \\ \varphi_{q r}=L_{r} \times i_{q r}+L_{m q} \times i_{m q}\end{array}\right. \\ \left\{\begin{array}{l}\varphi_{d 1}=-L_{s} \times i_{d 1}-L_{m} \times\left(i_{d 1}+i_{d 2}\right)-L_{d q} \times i_{q 2}+L_{m d} \times i_{m d} \\ \varphi_{q 1}=-L_{s} \times i_{q 1}-L_{m} \times\left(i_{q 1}+i_{q 2}\right)+L_{d q} \times i_{d 2}+L_{m q} \times i_{m q} \\ \varphi_{d 2}=-L_{s} \times i_{d 2}-L_{m} \times\left(i_{d 1}+i_{d 2}\right)+L_{d q} \times i_{q 1}+L_{m d} \times i_{m d} \\ \varphi_{q 2}=-L_{s} \times i_{q 2}-L_{m} \times\left(i_{q 1}+i_{q 2}\right)+L_{d q} \times i_{d 1}+L_{m q} \times i_{m q}\end{array}\right.\end{array}\right.$     (20)

The necessary condition for self-priming is [22]:

$C \succ \frac{1}{L_{s} \times \omega_{s}^{2}}$    (21)

For a slip close to zero, the speed is very close to that of synchronism, which gives [22].

$C=\frac{1}{L_{s} \times \omega_{r o t}^{2}}$    (22)

In practice, only the value of Cmin is important and beyond Cmax, the operation becomes unstable.

2.5 Centrifugal pump modeling

The centrifugal pump is a flow generator that ensures the movement of a fluid from one point to another, when gravity does not perform this task.

In practice, hydraulic engineers "make their work easier", using simple formulas close to theory where, knowing the flow rate Q and TDH, they can characterize the pumping system. With ηtotpumpengineinverter and 0.367 as an unity corrector, the electrical power required is given by:

$P_{\text {delivred }}=\frac{Q \times T D H}{0.367 \times \eta_{\text {tot }}}$    (23)

With, Kr: Proportionality coefficient, ωr: rotation speed, the centrifugal pump opposes a resistant torque from which its expression is given by [6]:

$T_{r}=K_{r} \omega_{r}^{2}+T_{s}$    (24)

To limit pressure drops and reduce energy costs, it is recommended not to exceed the water circulation speed in the piping of 0.5 m/s and for this, larger diameter tubes are used.

The recommended diameter is:  

$d=25 \times Q$    (25)

And the flow velocity is obtained by:

$v_{\text {flow }}=\frac{350 \times Q}{d^{2}}$    (26)

The pump can maintain excellent performance, providing a different flow rate and TDH, as long as the speed is changed.

The laws of similarity allow the deduction of the flow rate, the TDH and the power of the pump or of another pump in the case where the speed of the pump changes from a value N1 to a value N2 [11]:

The new flow, the new TDH and the new engine power are obtained by:

$\left\{\begin{array}{c}Q_{2}=Q_{1} \times \frac{N_{2}}{N_{1}} \\ T D H_{2}=T D H_{1} \times\left(\frac{N_{2}}{N_{1}}\right)^{2} \\ P_{2}=P_{1} \times\left(\frac{N_{2}}{N_{1}}\right)^{3}\end{array}\right.$    (27)

3. Sizing of a Stand-Alone Installation

For the supply of drinking water to a village located in a desert area not connected to the conventional electricity grid, the use of solar photovoltaic pumping and wind power is an attractive long-term solution.

Indeed, a water tower with a capacity of 150 m3, sufficient for the daily needs of the inhabitants, was erected in order to draw water from the only well in this area.

For nominal flow Qn=30m3/h, a TDH=17m, ηpump=0.55, ηengine=0.85, ηinverter=0.9, the recommended diameter of the pipes is:

$d=25 \times Q=25 \times 30=750 \mathrm{~mm}$

The pumping time is:

$T_{\text {pumping }}=\frac{V}{Q_{n}}=\frac{150}{30}=5$ hours

The total efficiency of the installation is:

$\eta_{\text {tot }}=\eta_{\text {pump }} \times \eta_{\text {engine }} \times \eta_{\text {inverter }}=0.55 \times 0.85 \times 0.95=0.444$

The electric power delivered is:

$P_{\text {delived }}=\frac{Q \times T D H}{0.367 \times \eta_{\text {tot }}}=\frac{30 \times 17}{0.367 \times 0.444}=3130 \mathrm{~W}$

The daily energy required is:

$E_{c}=P_{\text {delved }} \times T_{\text {pumping }}=3130 \times 5=15650 \mathrm{Wh} / \mathrm{d}$

The power losses attributable to temperature and dust represent one fifth of the power delivered by all the modules, the power of the GPV is:

$P_{g}=\frac{E_{c}}{T_{\text {pumping }} \times\left(1-\sum \text { losses }\right)}=\frac{15650}{5 \times(1-0.2)}=3912.5 \mathrm{~W}$

The model used is the SIEMENS SM 110-24 type panel, having a standardized nominal power of 110Wp, the number of panels to be used is:

$N \geq \frac{P_{g}}{P_{\text {panel }}}=\frac{3912.5}{110}=35.55$ panels

The number of panels is, therefore, 36 panels.

To obtain the electrical energy equivalent to 36 photovoltaic panels, or 3960W, a three-bladed wind turbine operating at fixed speed is used in this region where the wind speed is average 6.5 m/s. The DSIG used for the conversion has an efficiency of 0.88 with a slip of -1% and a speed multiplier having an efficiency of 0.9. The mechanical power required to rotate the wind turbine blades is:

$P_{M e c}=\frac{P_{e l e c}}{\eta_{\text {Multi }} \times \eta_{D S I G}}=\frac{3960}{0.9 \times 0.88}=5000 \mathrm{~W}$

From the characteristic of the three blades wind turbine, the corresponding coefficients are Cp = 0.48 and λ = 8 [16].

From relation 12, we obtain the length of the blades as follows:

$R=\left(\frac{2 \times P_{M e c}}{\rho \times \pi \times C_{p} \times V^{2}}\right)^{\frac{1}{3}}=\left(\frac{2 \times 5000}{1.22 \times \pi \times 0.48 \times 6.5^{2}}\right)^{\frac{1}{3}}=5.04 \simeq 5 m$

The speed of the blades being:

$N=\frac{30 \times \lambda \times V}{\pi \times R}=\frac{30 \times 8 \times 6.5}{\pi \times 5}=98.36 \mathrm{rpm}$

The multiplying coefficient is thus obtained by:

$K=\frac{N_{s}}{N}=\frac{1500}{98.36}=15.25$

So the wind turbine used has blades with a length of 5 m, a speed multiplier with a ratio K = 15.25.

4. Results and Comments

In the interval [0s-3s], the GPV supplies the DC bus to the two inverters used to supply the DSIM which will drive the centrifugal pump.

In the interval [3s-5s], the necessary power is no longer guaranteed by the GPV, hence the need to resort to the wind generator by offering DC bus necessary after electrical rectification of the voltages generated by the DSIG with a wind made up of an oscillating component, varying around an average component of 6.5 m/s.

4.1 Pump simulation results

At start-up, Figure 4 shows that the electromagnetic torque reaches a peak of 26 Nm before reaching the resistive torque of the pump with an oscillating value of ± 2Nm around the torque of the pump which is 12 Nm.

Figure 4. Electromagnetic & pump torques

Figure 5. Rotative & synchronism speed

Figure 6. Characteristic flow – TDH

Figure 7. Characteristic Torque-speed & TDH-speed

Figure 8. Characteristic flow - speed

Figure 5 and Figure 6 shows that the flow changes in the same way as the TDH and which is similar to the speed.

On the other hand, Figure 7 shows that the variation of the TDH is similar to that of the resistive torque which obeys, suitably, the variation as a function of the square of the speed of rotation in agreement with the relation 24.

Figure 8 shows that before reaching a speed of 150 rad/s, the pump piping does not provide any flow, then the flow increases with increasing rotational speed.

4.2 DSIG simulation results

Thus, the DSIG is first tested at no-load and then tested with a resistive load to simulate rectification.

The value of the self-priming capacitors, represented by Figure 9, has an effect on the voltage supplied. We opted for C = 40μF.

Figure 9. Diagram of a DSIG-based energy conversion

4.2.1 Simulation of the no-load DSIG

The rotor of the DSIG is driven at no load (without omitting the capacities) at a speed appreciably higher than the speed of synchronism.

Figures 10 and 11 shows, that in the presence of a remanent field, it is observed at the terminals of the two stars of the stator a voltage and a current which evolve exponentially before reaching a maximum voltage of 227.5 V and a current of 2.86 A.

At start-up, Figure 12 shows than the magnetizing inductance Lm takes a value of 0.14 Henry and increases slightly then decreases when the equilibrium state is established to stabilize at a value of 0.108H, on the other hand than the magnetizing current increases from 0 to 7 A.

Figure 10. Voltages generated without load

Figure 11. Current generated without load

Figure 12. Magnetizing inductance & current

Figure 13 reveals than the rotor current also increases and draws a sinusoidal shape with a maximum value of 0.14 A with a period Trotor = 12.46 s equivalent to a frequency mainly due to the slip of low value, approximately, close to zero, which reflects the no-load operation mode.

Figure 13. Rotorique current without load

Figure 14. Lissajous curve

Figure 14 clearly shows the phase shift existing between the voltage and the current delivered at the terminals of the two stars of the stator. The circular Lissajous curve indicates that the phase shift is 90°, which confirms the operation without load but with the presence of the self-priming capacitors.

4.2.2 Simulation with a purely resistive load

In this test, at t = 3s, a balanced resistive load of 200 Ω is inserted at the generator output.

Figure 15 reveals that the magnetizing inductance Lm increases from 0.108 H to a fluctuating value between 0.126 H and 0.127 H and that the magnetizing current decreases by 7 A to reach a floating value between 4.53 A and 4.72 A.

When the load is connected, Figure 16 shows that the phase-to-neutral voltage across the two stars of the stator decreases to reach 168.4 V and Figure 17 shows the decrease in current from 2.86 A to 2.22 A and Figure 18 gives a current of 0.83A which travels through the three resistances of the load.

The increase in the active power supplied by the generator is the cause of the increase in the currents induced in the rotor. Figure 19 shows the sinusoidal shape of the currents induced in the rotor having 2A as maximum value and 1.4 Hz as frequency.

Figure 15. Magnetizing inductance & current

Figure 16. Voltages generated with resistive load

Figure 17. Current generated with resistive load

Figure 18. Resistive load current

Figure 19. Rotorique current with resistive load

Figure 20. Voltage and current across the resistive load

Figure 20 indicates that the voltage and the current are in phase, that is to say a zero phase shift.

4.2.3 Influence of the self-priming capacitor

In order to establish the influence of the values of the self-starting capacitors on the characteristics of the machine, we carried out simulations with capacities from 35 μF to 55 μF with a step of 5 μF.

Figure 21. Influence of self-priming capacitors on the magnetizing current

Figure 22. Influence of self-priming capacitors on magnetizing inductance

Figure 21 summarizes the various forms of the magnetizing current which increases from 4.63 A for C=35 μF to 11.29 A for C=55 μF, contrary to what is shown in Figure 22 which shows that the value of the magnetizing inductance decreases as and as the value of C increases.

Table 1 shows that voltage, current and rotor current increase with the selection of a larger value of the self-priming capacitors. It is also interesting to add that the response time, decreases from t = 2 s for C = 35 μF to t = 0.4 s for C = 55 μF.

These results clearly demonstrate that the performance of the machine is clearly influenced by the values of the self-priming capacities. The choice made on C = 40 μF is not fortuitous but is in direct relation with the nameplate of the DSIG, in particular the current that must be supplied at a certain speed of rotation.

Table 1. Self-priming capacitor influency

$C[\mu F]$ 

tr [s]

Lm [H]

im [A]

vs [V]

is [A]

ir [A]

35

2.0

0.1260

04.63

171.5

1.89

0.099

40

1.0

0.1087

07.00

228.0

2.86

0.142

45

0.6

0.0950

08.67

250.5

3.54

0.186

50

0.5

0.0845

10.05

262.5

4.10

0.32

55

0.4

0.0754

11.29

268.0

4.61

0.42

4.2.4 Influence of the resistance value

In order to establish the influence of the values of the load resistance on the characteristics of the machine, we carried out simulations with resistances from 150 Ω to 300 Ω with a step of 50.

Figure 23 shows that as the value of R increases, the magnetizing current im increases from 3.10 A for R = 150 Ω to 5.78 A for R = 300 Ω.

Figure 23. Influence of the resistance on the magnetizing current

Table 2. Load resistance influency

$\mathbf{R}[\Omega]$

Lm [H]

im [A]

vi [V]

ii [A]

ir [A]

150

0.1350

3.10

112.00

1.54

1.78

160

0.1334

3.44

129.00

1.77

1.96

170

0.1312

3.84

142.00

1.92

2.00

200

0.1270

4.71

167.50

2.22

2.02

210

0.1254

4.81

172.00

2.27

2.00

220

0.1243

4.96

177.00

2.32

1.95

250

0.1225

5.40

187.60

2.42

1.84

300

0.1198

5.78

194.80

2.48

1.65

Table 2 summarizes the various parameters governing the operation of the DSIG under resistive load with the various resistance values. Thus, the voltage supplied and the current supplied increase with the increase in the value of the resistance. On the other hand, the rotor current reaches maximum values for a resistance range varying between 170 Ω and 210 Ω.

These results demonstrate that the performance of the machine is clearly influenced by the values of the load resistance.

4.2.5 Velocity influency

In order to establish the influence of the variation of the drive speed on the characteristics of the generator, a simulation with speeds close to that of synchronism with a step of 5.5 rad/s are carried out.

Figure 24 shows that if the driving speed is increased, the magnetizing current increases from 4.62 A for a speed of 314.5 rad/s to a value of 5.92 A for a speed of 325.5 rad/s.

Figure 25 summarizes the evolution of magnetizing inductance which, unlike magnetizing current, decreases as speed increases. Figure 26 shows the evolution of the rotor current which increases with increasing speed. The same behavior is observed for the voltages supplied and the currents supplied.

Figure 24. Speed influency on the magnetization current

Figure 25. Speed influency on the magnetizing inductance

Figure 26. Speed influency on the rotor current

Table 3. Velocity influency

N[rd/s]

Lm [H]

im [A]

vs[V]

is [A]

ir [A]

f [Hz]

314.5

0.1270

4.71

168

2.21

2.02

50.05

320.0

0.1226

5.44

190

2.55

2.30

50.93

325.5

0.1181

6.04

208

2.83

2.56

51.81

Table 3 summarizes the operation of this machine when varying the drive speed. These results demonstrate that the performance of the DSIG is clearly influenced by the values of the drive speed.

5. Conclusion

Designing and building a pumping station is a complex task, which must take into account the constraints resulting from hydraulics, the pricing of the supply of electrical energy, while ensuring a good balance between investment and the cost of operation.

The choice of pump should be based on the analysis of demand and its daily and seasonal fluctuations and the possibility of expansion in the future.

Fluctuations in the supply of electrical energy can vary considerably, depending on the period of consumption, it is necessary to store water in tanks to maintain the distribution.

Solar pumping is an interesting technology for a maximum flow of 100 m3/d at TDH = 10 m. Beyond that, the surface area of the solar panels to be installed quickly becomes large and the installation very expensive.

To meet the energy needs in isolated areas, the wind is one of the ideal energy vectors to replace fossil fuels in the long term and the introduction of photovoltaic energy becomes a necessity and the use of hybrid system becomes a necessity absolute to achieve filling the gaps of each renewable source of the hybrid system.

The results obtained clearly indicate that the combination of these two sources in this region allows us to meet the drinking water needs of the locality, either during the day when the sunshine provides sufficient energy for pumping or at nightfall when the wind is blowing enough to obtain desired flows. Notwithstanding the use of dual star induction machines, as a generator or as a motor, which ensure operation in degraded mode in the event of phase losses.

Nomenclature

AC/DC

Converter

DC/AC

Inverter

DC/DC

Converter

DSIG

Dual stator induction generator

DSIM

Dual stator induction motor

GPV

Photovoltaic generator

HPS

Hybrid pumping system

PV

Photovoltaic

C

Self priming capacitor

Cp

Power exchange coefficient

C1, C2

Constants

d

Inside diameter of the conduit

Ec

Daily energy

frotor

Rotor frequency

Fr

Coefficient of friction

Gs

Sunshine

Gsref

Sunshine referency

I

Moment of inertia

Icc

Short-circuit current

Id & iq

Direct & quadratic current

im

Magnetization current

Im

Current at maximum power

Imref

Referency current at maximum power

ir,abc

Rotor current

i1,abc/ i2,abc

Currents of star 1and star 2

K

Multiplying coefficient

Kr

Proportionality coefficient

Lm

Magnetizing inductance

Lr

Rotor inductance

Ls

Stator inductance

Lx,y 

Mutual inductance

N

Pump rotation speed

p

Number of pole pairs

Pdelivred

Electrical power

Peol

Aerodynamic (turbine) power

Pmec

Mechanical power

Ppanel

Normalized power

Q

Flow

R

Blade length

rr

DSIG rotor resistor

rs

DSIG stator resistor

Rr

DSIM rotor resistor

Rs

DSIM stator resistor

T

Temperature

TDH

Total dynamic head

Tem

Electromagnetic torque

Tj

Cell junction temperature

Tjref

Refrency cell junction temperature

Tpumping

Pumping time

Tr

Resistant torque

Ts

Static torque

Trotor

Rotor period

TT

Turbine torque

V

Wind velocity

Vt

Thermal voltage

Vdr, Vqr

Direct & quadratic voltage

vflow

Flow velocity

Vm

Maximum power voltage

Voc

Open circuit voltage

v1,abc

Stator voltage of star 1

v2,abc

Stator voltage of star 2

Greek symbols

α, β

Constant parameters

ΔIm

Temperature coefficient of current

ΔVm

Temperature coefficient of voltage

θe, θm

Electric & mechanical angle

ηengine

Engine efficiency

ηinverter

Inverter efficiency

ηmulti

Multiplier efficiency

ηpump

Pump efficiency

λ

Specific speed

ρ

Air density

φd,φq

Direct & quadratic fluxes

φr,abc, φr

Rotor fluxes

φ1,abc, φs1

Stator fluxes of star 1

φ2,abc, φs2

Stator fluxes of star 2

ωmag

Magnetic energy

ωr

Rotation speed

ωrotor

Rotor pulsation

ωs

Stator pulsation

Ω

Angular speed

ΩT

Turbine angular speed

Appendix

Photovoltaic panels SIEMENS SM 110-24

Designation

Value

Panel maximal power.

POP =110 W

Current at the maximum power point.

IOP =3.15 A

Voltage at the maximum power point.

VOP =35 V

Current of short circuit

ICC =3.45 A

Open circuit voltage

VCO =43.5 V

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