# Optimized and Sustainable PV Water Pumping System with Three-Port Converter, a Case Study: The Al-Kharijah Oasis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. System Modeling

#### 3.1. PV Array

_{ser}× N

_{par}modules [13,14]:

#### 3.2. Non-Isolated Three-Port DC–DC Boost Converter

_{pv}), load is connected to the output port (V

_{o}), and the battery is connected to a bidirectional port in a single circuit (V

_{b}). The TPC reduces the conversion stages, so the system is more efficient, has small packing, and a unified central power management is applied through three ports. Figure 3 shows a schematic diagram of the TPC [15].

#### 3.3. Modes of Operation and Power Flow for TPC

_{PV}), the load power (P

_{out}), and the bidirectional power of the battery (P

_{battery}). According to the power–balance principle, the relation between the three ports’ power is obtained as [15]; TPC operating modes are determined based on the difference between P

_{PV}and P

_{battery}as described in Figure 4.

_{PV}–P

_{load}).

#### 3.3.1. Dual Output Mode

_{1}is ON, S

_{2}and S

_{3}are OFF, is valid for a time interval of D

_{1}× T

_{s}. Mode II, when S

_{2}is ON and S

_{1}and S

_{3}are OFF, is valid for a time interval of D

_{2}× T

_{s}. In mode III, all switches are OFF and it is valid for a time interval of (1 − D

_{1}− D

_{2}) × T

_{s}. Figure 6 describes the circuit diagram in the Dom mode:

#### 3.3.2. Dual Input Mode (Dim)

_{pv}is less than the load power, PV and batteries share together to feed the load, which is called Dim mode. There are two cases in the Dim mode, when D1 > D3, and when D1 < D3.

_{1}and S

_{3}are ON, and S

_{2}is OFF is for a time equals D

_{3}×T

_{s}. Mode II’s interval is for a time (D

_{1}− D

_{3}) × T

_{s}, where S

_{1}is ON, and S

_{2}and S

_{3}are OFF. Mode III’s interval is for a time (1 − D

_{1}) × T

_{s}, in which S

_{1}, S

_{2}, and S

_{3}are OFF.

_{1}× T

_{s,}in which S

_{1}and S

_{3}are ON, and S

_{2}is OFF. The mode II interval equals (D

_{3}− D

_{1}) × Ts, where S

_{3}is ON, and S

_{1}and S

_{2}are OFF. The mode III interval equals (1 − D

_{3}) × Ts, in which S1, S

_{2}, and S

_{3}are OFF.

_{Dim}average matrix. Similarly, due to the matrices B

_{Dim}, C

_{Dim}, and E

_{Dim}, the state-space averaged model of the TPC in Dim can be expressed as [15]:

#### 3.3.3. Single Input Single Output PV to Load (Siso)

_{1}× T

_{s,}where S

_{1}is ON, S

_{2}and S

_{3}are OFF. The mode II interval equals (1 − D

_{1}) × T

_{s}, where S

_{1}, S

_{2}, and S

_{3}are OFF. Figure 8 shows circuit diagram for the PV to load mode.

#### 3.3.4. Single Input Single Output Battery to Load (Siso)

_{1}×T

_{s,}in which S

_{1}and S

_{3}are ON, but S

_{2}is OFF. Mode II interval is for a time (1 − D

_{1}) × T

_{s}, where S

_{3}is still ON but S

_{1}and S

_{2}are OFF. Figure 9 shows circuit diagram for the battery to load mode.

#### 3.4. Modelling of Three-Phase Induction Motor

_{stator}components i

_{sd}, i

_{sq}, λ

_{rd}, and ω

_{r}. The continuous state-space model for (IM) is shown as the following [16]:

_{sd}i

_{sq}λ

_{rd}ω

_{r}]

^{T}; u ∈ $\Re $ (2 × 1) is an input vector consisting of terminal voltage, indicated by u = [V

_{sd}V

_{sq}]

^{T}; δ ∈ $\Re $

^{(4 × 1)}is the disturbance vector, given by δ = [0 0 0 (−p/J

_{t})T

_{l}]

^{T}, with J

_{t}that is total inertia moment of coupled rotating parts; and A(x) ∈ $\Re $

^{(4 × 4)}is the matrix characteristics of the system, given by [16]:

_{m}is the magnetizing inductance; and ω

_{s}is the synchronous speed (rad/s), as following [16]:

_{slip}is the slip speed. B ∈ $\Re $ (4 × 2) is input matrix given by [16]:

_{rd}ω

_{r}]

^{T}; output matrix C ∈ $\Re $

^{(2 × 4)}is given by

#### 3.5. Pump Modelling Equations

## 4. Control Strategies and Optimization

#### 4.1. Control Strategies

- PV power. Fuzzy logic is applied to gain maximum power from the PV array.
- A PI controller is used with the battery to regulate the DC bus voltage at reference value.
- A PI controller shall be used with the inverter to obtain a pure sinusoidal wave at the load terminals.

#### 4.2. Optimization

_{DC}− V

_{load}.

## 5. System Design

^{3}/h, so total consumption is 4.1 m

^{3}/h. Water pump parameters are selected and shown in Table 2. IM parameters are selected to be suitable enough to drive the water pump. The average solar energy throughout the year in the Al-Kharijah oasis is shown in Figure 14; also, Figure 15 shows the average number of daylight hours throughout the year [21].

_{pv}can be calculated at head height 65 m with the following equation [22,23]:

^{2}), ${\rho}_{s}$ = 1000 (kg/m

^{3}), Q

_{s}= 20 (m

^{3}/day/house), G = 6.9 (kW/m

^{2}), T

_{h}= 65 (m), ${\eta}_{p}$, and $\rho $

_{1}for the pump are selected from [24], Substitute in Equation (17) then, P

_{pv}= 5.7 kW. The PV array consists of five parallel strings, and six series modules per string. PV module data and TPC circuit parameters are calculated and listed; motor parameters are selected as shown in Table 2 [25].

**Table 2.**System parameters [25].

PV module power (W) | 195.4 |

V_{oc} open circuit voltage (V) | 45 |

I_{sc} short circuit current (A) | 5.56 |

Voltage at maximum power (V) | 37.5 |

Current at maximum power (A) | 5.21 |

Number of cells per module | 72 |

Battery type | Lithium-ion |

Battery nominal voltage (V) | 12 × 25 |

Initial state of charge (%) | 75 |

Rated battery capacity (AH) | 250 |

Capacitor C_{in} (µF) | 300 |

Inductor L_{f} (mH) | 3 |

Capacitor C_{o} (µF) | 500 |

Motor rated power (hp) | 5.5 |

Motor nominal voltage (V) | 400 |

Motor rated speed (rpm) | 1430 |

Pump rated power (hp) | 5 |

Max. head height (m) | 95 |

Pump body material | Stainless steel |

## 6. Simulation Results and Discussion

**Case study I: Dual output mode**(**Dom**)

^{2}. The PV output power is high enough to operate the motor, with excess power to charge the batteries; the motor operates at rated torque 27 N.m. The previously discussed control technique manages to set the DC bus voltage to 600 V, as shown in Figure 16a. The maximum DC bus ripple factor voltage percentage equals nearly 0.8%, as shown in Figure 16b.

^{2}as MPPT is applied and PV power is at the maximum value; also load power equals 4 kW. It can be noticed that actual motor speed and actual PV power are at the rated values. Figure 20 shows Dom mode power management. It shows PV power, load power, and battery state of charge versus time, where the excess PV power charges batteries.

**Case II: Dual input mode**(**Dim**)

^{2}and the motor operates at rated torque, so the PV output power is not high enough to operate this load, as PV equals nearly 1.6 kW; hence, the battery supplies more power. Figure 21 shows DC bus voltage and DC bus ripple factor. The DC bus ripple factor equals nearly 3%, which is higher than the Dom case, as in the Dim case, PV feeds load with less power than the Dom case; load is fed by both PV and batteries.

**Case III: Single input single output Siso**(**battery to load**)**:**

**Case IV: Simulation for**(**Dom-Dim-Siso battery to load**)**Modes Simultaneously**

^{2}, at Dim irradiation is 300 W/m

^{2}, and at the Siso no sun irradiation is available.

^{2}in the Dom mode, 1.6 kW/m

^{2}in the Dim mode, and zero in the Siso battery to load mode. The motor power equals nearly 2.2 kW as it works at a reduced torque of 15 N.m. The motor runs at a speed rate of 1430 as inverter output voltage is controlled at 380 V. Figure 36 shows the battery state of charge, where the battery charges in the Dom mode and discharges in the Dim and Siso modes.

**Case study**(**V**)**Al-Kharijah Oasis**

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A_{Dom} | System matrix during Dom |

A_{Dim} | System matrix during Dim |

B_{Dom} | Input matrix during Dom |

B_{Dim} | Input matrix during Dim |

C_{o} | Output capacitor (F) |

C_{b} | Battery capacitor (F) |

C_{in} | Input capacitor (F) |

C_{Dom} | Output matrix during Dom |

C_{Dim} | Output matrix during Dim |

D1 | Duty cycle for switch 1 |

D2 | Duty cycle for switch 2 |

D3 | Duty cycle for switch 3 |

${d\xb0}_{1}$ | Small signal perturbation |

${d\xb0}_{2}$ | Small signal perturbation |

D_{Dom} | Feedforward matrices during Dom |

D_{Dim} | Feedforward matrices during Dim |

g | Gravity acceleration (m/s^{2}) |

H | Total head in (m) |

I_{d} | Diode current (A) |

I_{pv} | PV current (A) |

I_{0} | Average output current (A) |

J_{t} | Total inertia moment (kg.m^{2}) |

L^{′}_{s} | Stator Transient inductance (H) |

L_{r} | Rotor inductance (H) |

N_{par} | Number of parallel modules |

N_{ser} | Number of series modules |

P_{pv} | PV input power (W) |

P_{out} | Load power (W) |

P_{battery} | Battery power (W) |

Q | Flow rate in (m^{3}/s) |

R_{b} | Battery resistance (Ω) |

R_{in} | Input resistance (Ω) |

R_{p} | Parallel resistance (Ω) |

R_{s} | Series resistance (Ω) |

R_{L} | Load resistance (Ω) |

V_{o} | Output voltage (V) |

V_{pv} | PV input voltage (V) |

V_{cin} | Input capacitor voltage (V) |

V_{cb} | Battery capacitor voltage (V) |

V_{Lf} | Inductor voltage (V) |

Vgs1 | Gate signal voltage across switch 1 (V) |

Vgs2 | Gate signal voltage across switch 2 (V) |

Vgs3 | Gate signal voltage across switch 3 (V) |

X^{*} | Currently Jellyfish with best location in the swarm |

$\tau $^{′}_{r} | Rotor transient time constant |

$\tau $^{′} | Transient time constant |

$\tau $_{r} | Rotor time constant |

α | Diode ideality constant |

ρ | Fluid density (kg/L) |

${\eta}_{p}$ | Pump efficiency (%) |

${\rho}_{l}$ | System losses (%) |

µ | Mean location of all jellyfish |

β | Distribution coefficient |

γ | Motion coefficient |

ꬾr_{d} | Rotor flux (T) |

λ_{rd} | Rotor flux (Wb) |

ω_{s} | Synchronous speed (rad/s) |

ω_{r} | Motor speed (rad/s) |

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**Figure 2.**The PV array has Nser and Npar modules [13].

**Figure 4.**TPC operating modes [15].

**Figure 11.**JF movements in ocean [19].

**Figure 14.**Average daily incident shortwave solar energy in Al-Kharijah [21].

**Figure 15.**Hours of daylight and twilight in Al-Kharijah [21].

**Figure 17.**(

**a**) RMS value of three-phase AC output voltage. (

**b**) RMS value of three-phase AC output current.

**Figure 27.**(

**a**) RMS value of three-phase AC output voltage. (

**b**) RMS value of three-phase AC output current.

**Figure 33.**(

**a**) RMS value of three-phase AC output voltage. (

**b**) RMS value of three-phase AC output current.

**Figure 37.**Solar irradiation for a day in August [21].

**Figure 40.**(

**a**) RMS value of three-phase AC output voltage. (

**b**) RMS value of three-phase AC output current.

**Figure 44.**(

**a**) THD value of three-phase AC output voltage. (

**b**) THD value of three-phase AC output current.

Dom | Dim | Siso |
---|---|---|

K_{P1} = 50 | K_{P1} = 61.2 | K_{P3} = 62.9 |

K_{I1} = 30 | K_{I1} = 84.3 | |

K_{P2} = 109.2 | K_{P2} = 5 | |

K_{I2} = 86.9 | K_{I2} = 3 | K_{I3} = 121.9 |

K_{P3} = 82.7 | K_{P3} = 164.9 | |

K_{I3} = 28.3 | K_{I3} = 188.3 |

Time (S) | Irradiation W/m^{2} | PV Power (kW) | Battery power (kW) | Load Power (kW) | Duty Cycle (S1) | Duty Cycle (S2) | Duty Cycle (S3) |
---|---|---|---|---|---|---|---|

9 am | 750 | 5 | −2.8 | 2.2 | 0.4 | 0.7 | 0 |

11 am | 980 | 5.6 | −3.4 | 2.2 | 0.4 | 0.7 | 0 |

1 pm | 850 | 4.3 | −2.1 | 2.2 | 0.4 | 0.5 | 0 |

3 pm | 500 | 1.5 | +0.7 | 2.2 | 0.58 | 0.5 | 0 |

5 pm | 200 | 1 | +1.2 | 2.2 | 0.55 | 0 | 0.3 |

7 pm | 100 | 0.5 | +1.7 | 2.2 | 0.55 | 0 | 0.6 |

9 pm | 0 | 0 | +2.2 | 2.2 | 0.42 | 0 | 1 |

11 pm | 0 | 0 | +2.2 | 2.2 | 0.42 | 0 | 1 |

1 am | 0 | 0 | +2.2 | 2.2 | 0.42 | 0 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Selmy, M.; El sherif, M.Z.; Noah, M.S.; Abdelqawee, I.M.
Optimized and Sustainable PV Water Pumping System with Three-Port Converter, a Case Study: The Al-Kharijah Oasis. *Electricity* **2024**, *5*, 227-253.
https://doi.org/10.3390/electricity5020012

**AMA Style**

Selmy M, El sherif MZ, Noah MS, Abdelqawee IM.
Optimized and Sustainable PV Water Pumping System with Three-Port Converter, a Case Study: The Al-Kharijah Oasis. *Electricity*. 2024; 5(2):227-253.
https://doi.org/10.3390/electricity5020012

**Chicago/Turabian Style**

Selmy, Mohamed, Mohsen Z. El sherif, Miral Salah Noah, and Islam M. Abdelqawee.
2024. "Optimized and Sustainable PV Water Pumping System with Three-Port Converter, a Case Study: The Al-Kharijah Oasis" *Electricity* 5, no. 2: 227-253.
https://doi.org/10.3390/electricity5020012