Design, Modeling and Optimization of Hybrid Photovoltaic/Wind Turbine System with Battery Storage: Application to Water Pumping

Intermittent nature of wind and photovoltaic energy production complicates the continuous operating of an electrical renewable system. By storing or restituting the surplus energy when needed, an energy storage facility is necessary to balance the demand and the supply of power. As a result, hybrid systems being both environmentally friendly and safer, are designed [1, 2]. To obtain the maximum power point of solar panels [3-10] and wind turbines [11-17], a variety of MPPTs are used. They all aim to maximize the power, but differ from each other in their performances.

In this work, the modeling, design and optimization of a hybrid photovoltaic/wind turbine water pumping system with batteries is presented. Batteries are inserted to ensure the pump demand during the periods when there is neither solar irradiance nor high wind speeds. Measurements of the wind speed, temperature and solar radiation profiles were performed during four days belonging to different seasons (winter, spring, summer and autumn) using a data acquisition system at the laboratory. An application is made for water pumping during the different seasons in a coastal Mediterranean region. The proposed sizing method involves the annual monthly average of the total incident energy [1]. This approach allows us to determine the size of the two generators. The different parameters of PV, wind turbine and batteries are identified at the laboratory to use them in simulation and to obtain more realistic models. The strategy optimization for the PV system is made by three MPPT methods (Pertub. & Observ (P&O) [3-5], Incremental & conductance (IncCond) [6-8] and fuzzy logic controller (FLC) [9, 10]. And, for the wind turbine, three MPPT methods have been investigated (Optimal torque control (OTC) [11, 12], Gradient Method (GM) [13, 14] and Fuzzy logic controller (FLC) [15-17]. Subsequently to comparisons, the proposed optimization strategy is based on the FLC MPPT method for the two generators, owing to its better performances in terms of power, efficiency and response time. The results clearly demonstrate the practicality of the suggested method on various days corresponding to the different seasons (winter, spring, summer and autumn). The proposed supervision for the water pumping system is used to satisfy the level of the pump needs and to protect the batteries used.

1.png

Figure 1. System description

The monthly energy produced is denoted by E_pv,m for the PV generator and E_wind,m for the wind generator (m=1, ..., 12 are the number of the months during a year).

The area of the generators necessary to achieve full load coverage during the worst month is calculated as follows:

$S_{p v}=\max \left(\frac{E_{\text {Load }, m}}{E_{p v, m}}\right)$

$S_{\text {wind }}=\max \left(\frac{E_{\text {Load }, m}}{E_{\text {wind }, m}}\right)$       (1)

where,

$E_{p v}=\eta_{p v} \cdot S_{p v} \cdot E_{i r r}$

$E_{w i n d}=P_{w i n d}=(1 / 2) \cdot \rho \cdot S \cdot V_{w i n d}^{3} \cdot C_{p} \cdot \Delta t$

$E_{\text {Load }}=S_{p v} \cdot E_{p v}+S_{\text {wind }} \cdot E_{\text {wind }}$            (2)

with, S_pv: the PV total area, η_pv: the PV efficiency, E_irr: the solar irradiance on a tilted plane.

The monthly energy produced by the system per unit of area is denoted E_pv,m for the photovoltaic energy and E_wind,m for the wind energy and E_L,m represents the energy required by the load (where m=1, 2, ..., 12 are the months of the year). We have:

$\begin{aligned} E_{p v, m} &=\left(\sum_{m=1}^{12} E_{p v}\right) / 12 \\ E_{\text {wind }, m} &=\left(\sum_{m=1}^{12} E_{\text {wind }}\right) / 12 \\ E_{\text {Load }, m} &=\left(\sum_{m=1}^{12} E_{\text {Load }}\right) / 12 \end{aligned}$          (3)

The limit value f=1 implies that the load is totally supplied by the PV power, whereas f=0 means that the load is entirely supplied by the wind power.

Therefore, the areas of the two PV and wind generators are given respectively by:

$S_{p v}=f\left(E_{\text {Load,ave }} / E_{p v, a v e}\right) \\ S_{\text {wind }}=(1-f)\left(E_{\text {Load,ave }} / E_{\text {wind,ave }}\right)$                   (4)

The number of PV panels and wind turbine are determined by the following equations:

$S_{p v, \text { final }}=N_{p v} \cdot S_{p v, u n i t} \\  S_{\text {wind,final }}=N_{\text {wind }} \cdot S_{\text {wind,unit }}$        (5)

The average consumed energy is given by:

$E_{\text {load-ave }}=E_{p v, a v e} \cdot S_{p v, u n i t}+E_{\text {wind,ave }} \cdot S_{\text {wind }, \text { unit }}$        (6)

The different calculations are summarized in Table 1. It illustrates the possible configurations of the coupling of the photovoltaic system with the wind power system. After calculations, the different energies are found in Table 1: E_pv,m=31.59 kWh/m², E_wind,m=54.86 kWh/m² and E_Load,m=231.09 kWh.

Besides, in Table 2, it is noticeable that the only value that is closer to the load value (231.09 kWh) is 244.40 kWh, hence the optimal configuration corresponds to f=0.9 (six PV panels +one wind turbine). The calculation of the battery capacity gives two batteries of (100 Ah, 12V).

Table 1. Different possible configurations of PV and wind systems

Table 2. Calculation of the number of panels and wind turbine

The strategy optimization regarding the PV system is made by three MPPT methods (Pertub& Observ (P&O), Incremental & conductance (INCcond) and fuzzy logic controller (FLC). And for the wind turbine, three MPPT methods have been investigated: (Optimal torque control (OTC), Gradient Method (GM) and Fuzzy logic controller (FLC).

5.1 Pertub and observe method (P&O)

One of the most common traditional approaches is the P&O algorithm. Its operation is determined by the tracking step size of the voltage reference [1]. This method is very simple to be implemented and it does not require any knowledge of the photovoltaic parameters, but presents oscillations at steady state. The different steps are shown in Figure 5a.

When ΔP_pv>0 and ΔV_pv>0 thus ΔP_pv∕ΔV_pv>0, the duty cycle is incremented, D=D+ΔD.

When ΔP_pv>0 and ΔV_pv<0 thus ΔP_pv∕ΔV_pv<0, the duty cycle is decremented, D=D-ΔD.

When ΔP_pv=0 and ΔV_pv=0 thusΔP_pv∕ΔV_pv=0, we retain the duty cycle, ΔD=0, D=D.

5.2 Incremental conductance algorithm (IncCond)

This alternative technique for determining the MPP is based on the knowledge of the conductance of the solar generator change and of the effects on the position of the operating point when compared to a maximum power point [1]. Its principle is to compare the conductance and the incremental conductance and to decide when to increase or to decrease the PV voltage to reach the MPP where the derivative of the power is equal to zero. The disadvantage of this method with fixed step is its oscillations. The different steps of the algorithm are displayed in Figure 5b.

When ΔI_pv∕ΔV_pv>-I_pv∕V_pv, the duty cycle is incremented D, D=D+ΔD.

When ΔI_pv∕ΔV_pv<-I_pv∕V_pv, the duty cycle is decremented D, D=D-ΔD.

When ΔI_pv∕ΔV_pv=-I_pv∕V_pv, the duty cycle is retained D, ΔD=0, D=D.

5.3 Fuzzy logic controller (FLC)

Fuzzification, inference engine, and defuzzification are the three steps that constitute the FLC. The error and change in error are the two inputs of the controller system. Its flowchart is depicted in Figure 5c for PV generators and Figure 5d for wind generators. It optimizes the magnitude of the increment to procure fast and fine tracking. The system based on MPPT fuzzy logic controller is composed of two inputs that are the error E(k) and the change in the error CE(k). For the PV generator, we have:

$\left\{ \begin{matrix}   E(k)=\frac{{{P}_{pv}}(k+1)-{{P}_{pv}}(k)}{{{V}_{pv}}(k+1)-{{V}_{pv}}(k)}  \\   CE(k)=E(k+1)-E(k)  \\  \end{matrix} \right.$           (17)

For wind turbine generator the rules depend on the wind power variations and speed variations, which give a torque reference and a wind turbine reference speed:

$\left\{\begin{aligned} \Delta \omega_{T b} &=\omega_{T b}(k)-\omega_{T b}(k-1) \\ \Delta P_{T b} &=P_{T b}(k)-P_{T b}(k-1) \\ \omega_{T b-r e f} &=\omega_{T b}(k-1)+\Delta \omega_{T b}(k) \end{aligned}\right.$          (18)

where, P_Tb(k) and_Tb(k) are respectively the output turbine power and its rotational speed at sampled instants (k) and D_Tb,ref(k) the instant of reference speed.

5.4 Optimal torque control algorithm (OTC)

Optimal torque control will adapt the generator torque to its maximum at various wind speeds. However, the properties of the turbine have to be known. The OTC algorithm is depicted in Figure 5e. Optimal power, rotational speed and electromagnetic torque are given as:

$\left\{\begin{aligned} P_{T b-o p t}=&(1 / 2) \cdot\left(C_{p-o p t} \cdot \rho \cdot \pi \cdot R_{T b}^{2}\right) \cdot V_{\text {wind }}^{3} \\ & \omega_{o p t}=V_{\text {wind }} \cdot \lambda_{o p t} / R_{T b} \\ T_{e m-o p t}=&(1 / 2) \cdot\left(C_{p} \cdot \rho \cdot \pi \cdot R_{T b}^{5} / \lambda 3\right) \cdot \omega_{T b-o p t}^{2} \end{aligned}\right.$                 (19)

5.5 Gradient method algorithm (GM)

The search for the optimal point by this method does not need the knowledge of the parameters of the optimal tip speed ratio and maximal power coefficient. The reference turbine speed is increased to its maximum, resulting in maximum power. To act on the generator speed, we control the direction of variation of the ratio dP_Tb/dw_Tb (Figure 5f). When this ratio becomes equal to zero, the desired maximum power is reached. The algorithm requires the knowledge of the power and speed at all times. At the iteration k, the speed reference is increased or decreased by a fixed step Δω_Tb.

$d P_{T b} / d \omega_{T b}=d P_{T b} / d t .\left(\omega_{T b} / d P_{T b}\right)^{-1}$         (20)

5a.png

(a) P&O

5b.png

(b) IncCond

5c.png

(c) FLC for PV generator

5d.png

(d) FLC for wind generator

5e.png

(e) OTC

5f.png

(f) GM

Figure 5. Flowchart of P&O, IncCond and FLC in PV and wind generators, OTC and GM strategies

An application for water pumping is considered for the area of Bejaia, a coastal region in the east of Algeria. The daily average water use is 0.5 m³. The energy utilized per day is around 7445.51 Wh/day. The profile of the load is adjusted according to the following equation [21]:

$P_{\text {Load }}=P_{P V}+P_{\text {wind }} \pm P_{\text {batt }}$      (22)

We have already made an application for a wind turbine system with batteries [21] and the proposed supervision has performed well and given good results. The same method was also applied to a PV system with batteries [23, 24] and to another application involving a PV system with batteries and fuel cells [25]. The found results confirmed the feasibility of the proposed method. In this paper, an application to a hybrid water pumping system is sought. The proposed power management control (PMC) is shown in Figure 17.

17.png

Figure 17. Flowchart of the proposed PMC

There are eight operating modes suggested to satisfy the power.

The initial condition of the battery SOC is:

$\mathrm{SOC}_{\min }=30 \%\left\langle\mathrm{SOC}\left\langle\mathrm{SOC}{ }_{\max }=90 \%\right.\right.$        (23)

Mode 1 (M1): P_hyb=P_load and the height is less than the reference height, which corresponds to the maximum volume of water to be pumped. The motor pump unit is driven by photovoltaic and wind powers.

Mode 2 (M2): P_hyb<P_load, SOC≤30%, the height is lower than the reference height, which corresponds to the maximum volume of water to be pumped. The batteries are then disconnected, and as the requirement of the load has not been met, the latter is immediately unloaded.

Mode 3 (M3): This situation occurs when the height is less than the reference height, which corresponds to the maximum volume of water to be pumped, and P_hyb<P_load, SOC>30%. The batteries will compensate for the shortage of power.

Mode 4 (M4): It corresponds to a height lower than the reference height which corresponds to the maximum volume of water, and more P_hyb>P_load and SOC≤90%. The load will be driven by the electricity generated by the two generators. The remaining energy is used to recharge the batteries.

Mode 5 (M5): The height is lower than the reference height which corresponds to the maximum volume of water (P_hyb>P_load and SOC>90%). The load will be driven by the power generated by the two generators and the surplus will be dissipated in a dump load.

Mode 6 (M6): It occurs when the head is greater than or equal to the reference head, which corresponds to the maximum amount of water that can be pumped. There is no need to fill the tank in this case. Also P_hyb=0, the load as well as the batteries will be disconnected.

Mode 7 (M7): The height is greater than or equal to the reference height which corresponds to the maximum volume of water. There is no need to fill the water tank. Moreover P_hyb≠0 and SOC<90%. The power generated by the photovoltaic and wind generators will be used to charge the batteries.

Mode 8 (M8): The height is greater than or equal to the reference height which corresponds to the maximum volume of water. There is no need to fill the water tank. Moreover P_hyb≠0 and SOC>90%. In this case the batteries will be disconnected.

The simulation program is run under Matlab/Simulink environment. The chosen height is variable (Figure 18) and the power of the pump is of about 900 W (Figure 2).

18.png

Figure 18. Chosen reference heights

A water pumping was realized during 8.28 hours maximum for each day. The pump power is given in Figure 19. The state of charge and battery voltage are respectively shown (Figure 20 and 21). It can be observed that the batteries (in red color) have not been solicited much whatever the period of the year. Indeed, the solar irradiance and the wind speeds in this Mediterranean region are very complementary especially in the summer (strong solar irradiance and low wind speeds) and in the winter (high wind speeds and average solar irradiance).

19.png

Figure 19. Power of the water pumping

20.png

Figure 20. Battery state of charge

21.png

Figure 21. Battery voltage

The different powers of each day are as follows (Figure 22).

22a.png

(a) Summer day

22b.png

(b) Autumn day

22c.png

(c) Winter day

22d.png

(d) Spring day

Figure 22. Obtained different powers for each day

It can be noted that the batteries have not been solicited much whatever the period of the year. The SOC values vary between 53.1% and 90%. The batteries were protected due to the proposed power control and the pump was supplied during 8.28 hours per day. The different powers have been well managed and the pump has been supplied with less stress on batteries.