Battery-Assisted PV-Pumping System

Abstract

Photovoltaic (PV) water pumping systems convert solar radiation into electricity via PV panels to feed and drive electric pumps. The electrical energy is produced in DC form and must be adopted and then converted into alternating current by employing inverters. Batteries are used to store energy and to improve the system performance. Solar battery-assisted water pumping technology is on the long-run cost-effective and sure environment friendly. PV must be controlled to achieve the maximum power point operating condition. The state of charge of the battery should be observed to guarantee a safe and long battery working hours. In this chapter, a simple and efficient off-grid battery-assisted quasi Z-source inverter (QZSI) was developed in a PV-pumping system as a replacement to the traditional two-stage converter (boost converter + voltage source inverter). Analysis and mathematical model of QZSI has been presented. MPPT from the solar panels and the battery state of charge (SOC) are to be considered in determining controller’s parameters. The controller produces the shoot through duty ratio (D) and modulation index of the inverter (M). The inverter switching pattern is prepared based on the simple boost modulation technique. The performance of the system under study is verified via MATLAB/Simulink simulation.

1. Introduction

Integration of renewable energy sources into the electrical generation systems is badly needed because of environmental and economic considerations. Solar energy is, of course, one of the most promising alternatives. However, a solar energy panel suffers from its need to a large space, low overall efficiency, and high initial and erection costs. In order to get an acceptable overall system efficiency, the interfacing systems (i.e., voltage regulators, inverters, etc.) must attain a very high efficiency.

Standalone systems and grid connected systems are two kinds of solar energy harvesters. Standalone systems are used in areas and sites where the grid is not reachable. A standalone system needs to be assisted by an energy storage unit to ensure a continuous and a better power quality. On the other hand, there is no need to have an energy storage unit in grid connected systems. Moreover, the energy harvesters improve the grid capabilities. The grid connected systems, however, have their own complexity and cost represented by phase-locked loops (PLL) for synchronization, active ad reactive power control and extra protection circuits.

In 2003, the impedance source inverter (ZSI) was introduced as a single-stage inverter [1]. An impedance network is included separating the source and the main inverter bridge as shown in Figure 1. The inverter is controlled by the same PWM technique applied in traditional two-stage inverter. However, the DC link voltage can be boosted by utilizing the additional shoot-through (ST) states, where any or all of the inverter bridge legs can be shorted. The boosting factor is determined by the duration of the ST periods. A modified topology of Z-source inverters was introduced in 2008 namely; quasi Z-source inverter (QZSI). The new topology features, in addition to all the advantages of ZSI, smaller passive element requirements for the impedance network [1, 2].

Figure 1.

Impedance source inverter.

In literature, four main quasi Z-source inverters have been developed which feature several improvements when compared to the traditional ZSIs. The voltage-fed ZSI as well as the two QZS voltage-fed inverters, with similar properties to the ZSI, are shown in Figure 2(a, c, and e), while the current-fed ZSI as well as two QZS current-fed inverters are shown in Figure 2(b, d and f).

Figure 2.

Different topologies of Z-source and quasi Z-source inverters. a. Voltage-fed ZSI. b. Current-fed ZSI. c. Voltage-fed QZSI with continuous current. d. Current-fed QZSI with discontinuous current. e. Voltage-fed QZSI with discontinuous current. f. Current-fed QZSI with continuous current.

The QZSI topologies shown in Figure 2c and e, are of unidirectional nature as the voltage-fed ZSI. In order to gain the bidirectional property, the diode, D1 could be substituted by a switch bidirectional in conducting, unidirectional in blocking. The capacitor C₂ in QZSI, shown in Figure 2c has a lower voltage value than the same capacitor C₂ in ZSI shown in Figure 2a. In the QZSI circuit, illustrated in Figure 2e, both capacitors C1 and C2 have lower voltages. Input current in circuit in Figure 2c is continuous and discontinuous in circuit in Figure 2e. There is no need to include an input capacitance in the topology of the QZSI shown in Figure 2c, due to presence the input inductor, L₁. Input capacitance is essential in both topologies of voltage-fed ZSI and QZSI in Figure 2e.

Circuits in Figure 2d and f are current-fed QZSI topologies. The presence of the diode, D1, with its specified position, in both circuits of Figure 2d and f marks these topologies with bidirectional property.

Current rating of inductor L₂ in the QZSI shown in Figure 2d is lower than the current rating of L₂ in the ZSI shown in Figure 2b. Reduced passive component count is clearly noticed. The QZSI shown in Figure 2f has also lower current ratings for inductors L₁ and L₂.

A common DC rail between the source and inverter characterizes the four QZSI voltage-fed and current-fed topologies. Additionally, the four QZSI circuits have no disadvantages in comparison with the conventional ZSI basic circuits. The four QZSI topologies can replace ZSI topology in any application [3].

In this chapter, a quasi Z-source inverter shown in Figure 2c will be adopted. These inverters are capable of performing maximum power tracking and inversion with no need for extra DC-DC converter. Other important operating characteristic is that the QZSI is operated with continuous input current. This ensures continuous supply current in PV system to facilitate maximization of the energy harvested. In addition, the system will be equipped with an energy storage device integrated into its topology as shown in Figure 3. This feature is essential when operating at low PV power conditions. In order to operate under these conditions, an energy storage device capable of managing the load demand for a period of time is required. Different placements of the batteries are used in literature as shown in Figure 3. By shunting a battery with either of the two circuit capacitors, the pumping system can be powered smoothly regardless the variations or the fluctuations of PV panel output. Because of the unique impedance network of QZSI, there is no need to add any extra circuit to charge or discharge the battery.

Figure 3.

Topology of battery-assisted QZSI. (a) Option 1 (b) option 2.

The control of the QZSI becomes more complex if the battery is added to the topology. For the sake of keeping the battery lasts longer, the accurate control of the battery charging current should be carefully treated. However, many papers pay attention to other aspects, regarding energy (production and management), system (reliability, unit size and cost). In this research, battery charging control methodology for QZSI with energy storage will be presented along with controlling the output power of the inverter.

2. Analysis of quazi Z-source inverter

2.1 Battery-assisted QZSI

A topology improvement for the QZSI to be used in PV systems was introduced in [4, 5], where an energy storage device is added to the circuit without any extra circuitry depending on QZSI unique input impedance network. This is available also in Z-source inverters as shown in [6, 7, 8]. However, they experience discontinuous input current that is not desirable for PV system. Moreover, batteries suffer from higher voltage rating than that the one expected in the case of the ZSI. The QZSI topologies with storage units operate with continuous input current and so they have low voltage rating batteries.

2.1.1 Circuit analysis for battery parallel with C₂

The proposed QZSI with energy storage topology is shown in Figure 3(a). These types of inverters are operated in two states, namely firstly, the active state which is pointed to as (T₁), and secondly, the shoot-through state which is pointed to as (T₀). In each switching cycle, the periodic time is calculated as T = T₁ + T₀. The inverter is operated based on normal sinusoidal pulse width modulation (SPWM) during the active state. While a short circuit between terminal P and terminal N is formed during the shoot-through state. The specified QZSI LC network is actually acting as a step-up DC-DC converter. Such converter is controlled by the shoot-through state. The equivalent circuit for each of the states is given in Figures 4 and 5. These equivalent circuits are accurate and valid as long as the current through each inductor is continuous so that the diode is complementary with the shoot-through state [9].

Figure 4.

Non-shoot-through state of battery-assisted QZSI [9].

Figure 5.

Shoot-through state of battery-assisted QZSI [9].

2.2 Shoot-through state mode

This mode (the shoot-through state) will make the inverter short circuit. As a result, the diode is turned off due to the reverse-bias voltage. The equivalent circuit, representing this mode, is shown in Figure 5. During this time interval, the circuit equations are formed as follows:

$$C\frac{d{V}_{C1}}{\mathit{dt}}=i_B-i_{L2}$$E1

$$C\frac{d{V}_{C2}}{\mathit{dt}}=-i_{L1}$$E2

$$L\frac{d{i}_{L1}}{\mathit{dt}}=V_{\mathit{\text{in}}}+V_{C2}$$E3

$$L\frac{d{i}_{L2}}{\mathit{dt}}=V_{C1}$$E4

Where i_L1, i_L2 and i_B are the currents in inductors L₁ and L₂, and in battery, respectively; V_C1, V_C2 and V_in are the voltages across capacitors C₁, C₂ and PV panel, respectively; C is the capacitance of capacitors C₁ and C₂; L is the inductance of inductors L₁ and L₂.

2.3 Non-shoot-through state mode

In this mode, the inverter is free to follow any one of the six active (non-zero) states and two conventional zero states, which is known as the non-shoot-through state. The diode current is continuous. Figure 4 illustrates the equivalent circuit. During this time interval, the circuit equations are written as follows:

$$C\frac{d{V}_{C1}}{\mathit{dt}}=i_B+i_{L2}-i_d$$E5

$$C\frac{d{V}_{C2}}{\mathit{dt}}=i_{L1}-i_d$$E6

$$L\frac{d{i}_{L1}}{\mathit{dt}}=V_{\mathit{\text{in}}}-V_{C1}$$E7

$$L\frac{d{i}_{L2}}{\mathit{dt}}=-V_{C2}$$E8

Where i_d is the load current going to the inverter.

The average voltages and currents are calculated using the average model between both states. The average voltage in each inductor is equal to zero during one switching cycle (T). From these average inductor voltages equations equated to zero, the capacitor one and the battery voltage relationship are calculated. The average voltage across V_L1 during each switching cycle is given by

$$\left(V_{\mathit{\text{in}}}-V_{C1}\right)\left(1-D\right)+\left(V_{\mathit{\text{in}}}+V_{\mathit{\text{batt}}}\right)D=0$$E9

The average voltage across V_L2 during each switching cycle is given by

$$\left(-V_{\mathit{\text{batt}}}\right)\left(1-D\right)+V_{C1}D=0$$E10

Eqs. (9) and (10) can be solved simultaneously with respect to V_batt and V_C1 to obtain that

$$V_{\mathit{pn}}=V_{\mathit{\text{batt}}}+V_{C1}=\frac{1}{1-2D}{V}_{\mathit{\text{in}}}$$E11

For the active SPWM time, (T1), the effective inverter DC rail voltage can be calculated using the circuit configuration shown in Figure 4 as follows

$$V_{\mathit{\text{batt}}}=\frac{D}{1-2D}{V}_{\mathit{\text{in}}}\mathit{\text{and}}{V}_{C1}=\frac{1-D}{1-2D}{V}_{\mathit{\text{in}}}$$E12

$$-i_{\mathit{\text{batt}}}=i_{L2}-i_{L1}$$E13

To derive the line to neutral peak voltage equation, the traditional inverter relationship is used, (${\widehat{v}}_{\mathit{ac}}=\frac{V_{\mathit{pn}}}{2}M$). By combining this equation with Eq. (11), it is easy to calculate the AC output voltage as Eq. (14)

$${\widehat{v}}_{\mathit{ac}}=\frac{V_{\mathit{\text{batt}}}+V_{C1}=\frac{1}{1-2D}{V}_{\mathit{\text{in}}}}{2}\mathit{MB}$$E14

2.3.1 Circuit analysis for battery parallel with C₁

In this configuration, the battery will be placed across the capacitance C₁ as shown in Figure 3(b). The analysis conducted in the previous section will be repeated for this case to get the relevant equations [10].

2.4 Shoot-through state mode

This mode will make the inverter short circuit via any one phase leg, which is known as the shoot-through state. Consequently, the diode is turned off as the anode to cathode voltage is reversed. The equivalent circuit is shown in Figure 6. In this mode, the equations governing the circuit operation are formed as follows:

Figure 6.

Shoot-through equivalent circuit [10].

$$C\frac{d{V}_{C1}}{\mathit{dt}}=i_B-i_{L2}$$E15

$$C\frac{d{V}_{C2}}{\mathit{dt}}=-i_{L1}$$E16

$$L\frac{d{i}_{L1}}{\mathit{dt}}=V_{\mathit{\text{in}}}+V_{C2}$$E17

$$L\frac{d{i}_{L2}}{\mathit{dt}}=V_{C1}$$E18

2.5 Non-shoot-through state mode

In this mode, the inverter is free to follow any one of the six active (non-zero) states and two conventional zero states, which is known as the non-shoot-through state. The diode current is continuous. Figure 7 illustrates the equivalent circuit. During this time interval, the circuit equations are written as follows:

Figure 7.

Non-shoot-through equivalent circuit [10].

$$C\frac{d{V}_{C1}}{\mathit{dt}}=i_B+i_{L2}-i_d$$E19

$$C\frac{d{V}_{C2}}{\mathit{dt}}=i_{L1}-i_d$$E20

$$L\frac{d{i}_{L1}}{\mathit{dt}}=V_{\mathit{\text{in}}}-V_{C1}$$E21

$$L\frac{d{i}_{L2}}{\mathit{dt}}=-V_{C2}$$E22

Therefore, the average voltages and currents have the relationships as

$$V_{\mathit{pn}}=V_{\mathit{\text{batt}}}+V_{C2}=\frac{1}{1-2D}{V}_{\mathit{\text{in}}}$$E23

$$V_{\mathit{\text{batt}}}=\frac{1-D}{1-2D}{V}_{\mathit{\text{in}}}\mathit{\text{and}}{V}_{C2}=\frac{D}{1-2D}{V}_{\mathit{\text{in}}}$$E24

$$i_{\mathit{\text{batt}}}=i_{L2}-i_{L1}$$E25

The voltage V_C1 of capacitor C₁ will be approximately equal to the battery voltage V_batt if the voltage drop on the battery’s internal resistance is ignored. Thus, from Eqs. (23) and (24), the DC-link peak voltage V_pn will be

$$V_{\mathit{pn}}=2V_{\mathit{\text{batt}}}-V_{\mathit{\text{in}}}$$E26

The output power of the inverter can be controlled by manipulating the desired output voltage, while the output peak phase voltage of the inverter is the same like previous mode.

3. Design and control of battery-assisted QSZI

The power flow of the complete system is affected completely by actual conditions of battery state of charge. The control algorithm is branched into three main categories: battery management system; PV MPPT and motor control. A battery must be protected against overcharging or being depleted. This is achieved by adding a battery management system. PV MPPT is used to guarantee operation at MPPT condition. The motor control will achieve the power balance between the three main systems, namely PV panels, battery and pump.

3.1 Battery management system

Two cases are to be discussed according to the battery SOC:

The first case: the battery is in charging mode. The state of charge is at the possible minimum SOC level. The battery power and load power as the dependent variable are to be determined. It is assumed that proper sizing of the system parameters has been carried out. As a result, the power generated from PV will be less than the combined ratings of the load and battery together. The MPPT tracking system determines the duty ratio. The modulation index is selected based on the battery state of charge.

The second case: the battery is in discharging mode. The state of charge is at the possible maximum SOC level. The battery power and load power as the dependent variable are to be determined. Again, it is assumed that proper sizing of the system parameters has been carried out. As a result, the power generated from PV will be less than the combined ratings of the load and battery together. Similar to the first case, the MPPT tracking system determines the duty ratio, the modulation index is selected based on the battery state of charge.

The detailed algorithm of the battery management is shown in Figure 8. This figure is built to show the complete flowchart of the system when battery parallel with capacitor C₁.

Figure 8.

Complete flowchart of the system when battery parallel with capacitor C₁.

3.2 PV MPPT

The most famous method followed in MPPT calculations is perturb and observe. A small perturbation in the system is made. Accordingly, the effect of this perturbation on the power is observed. The main purpose is to maximize the power. If the response is positive (power increases), then apply the same amount of perturbation. The perturbation will be reversed if the response is negative (power decreases). This iteration continues until the system’s maximum power point is reached. Shoot-through duty ratio affects the system voltages as explained in Section 2, and so it is used as perturbation element. It is clear from Eq. (23) and Eq. (24) that there is a negative relation between the shoot-through duty ratio and the input voltage. This input voltage is the PV array voltage in the system under study. So, if it is required to increase (decrease) the PV array voltage, the duty ratio has to be decreased (increased).

Good performance in MPPT determination is achieved by the perturbation algorithms. It is simple to implement and can work even if the PV array information is missed. However, an action must be taken to stop the perturbation action when the system reaches the maximum power point. This is because the system continues to perturb around the maximum power point. This may affect the output waveforms quality and decrease the performance of the system generally.

The algorithm is implemented by setting an initial value of 0.05 duty ratio and a step of 0.001, and then, at each measurement the duty is changed by the step 0.001 until the algorithm reaches the final value. Flow chart of the algorithm is illustrated in Figure 9.

Figure 9.

Flowchart of P&O algorithm using duty ratio as perturbation [11].

3.3 Motor: pump set control

In pumping system, the continuity of the water flow, rather than the speed requirement, is considered to be more important. The more power consumed, the more water flow obtained. Power consumed by the load (motor–pump) comes from the power offered by both sources PV and storage batteries.

The motor is loaded by the water pump, and the load torque $T_L$ can be expressed mathematically by

$$T_L=k{\omega }_r^2$$E27

Where $k$ is the pump constant, and ${\omega }_r$ is the rotor speed.

The algorithm is implemented by setting an initial value of 0.8 for the modulation index (M) and a step of 0.001, and then, at each measurement the modulation index is perturbed by the step 0.001. The value of M is linearly proportional to the voltage and frequency of the motor. Hence, rated frequency (60 Hz) is proportional to M = 0.8, and if the modulation index decreased, the frequency is linearly decreased. As a consequence, the voltage is also decreased (460 V is proportional to 60 Hz) until the algorithm reaches the final value.

In scalar control, the control of the magnitudes of voltage and frequency leads to the control the torque and the magnetic flux of the motor. Induction motor has an inherent coupling effect. Motor-induced torque and magnetic flux are functions of voltage and frequency. Varying the applied voltage will affect both the induced torque and the magnetic flux. The dynamic performance of the scalar control got a weak point. However, scalar control implementation is simple. Then by using V/f control speed can be directly controlled. By controlling the torque and speed of the pump, the power consumed by the system is controlled [12].

The power consumed by the induction motor is given by

$$P_{\mathit{\text{in}}}=3V_s{I}_s\mathit{\text{coscos}}\phi =k{\omega }_r^3$$E28

where $V_s$ is the stator phase voltage,

$I_s$ is the stator current and

$\mathit{cos}\phi$ is the power factor

4. Simulation results

In this section, a model representing the PV-pumping system will be simulated to verify the control technique. The model was developed using MATLAB/Simulink environment as shown in Figure 10 [12].

Figure 10.

Simulink model of the PV-pumping system.

System parameters values at rated power conditions are listed in Table 1. Induction motor values have been taken from the MATLAB/Simulink. The supply frequency is 60 Hz. The PV array is selected to suit the motor loading condition given that the PV array is working at its maximum power. In the simulation, the PV array is treated as one unit. In reality, number of panels, power rating of each panel, and how they are electrically connected should be determined. The irradiance is assumed to be changed from 1000 to 500w/m² after 5 seconds. The simulation sample time is selected to be 1 μs, given that the switching frequency is 10 KHz, a shoot-through duty ratio resolution is 0.01. Each simulation run takes 2–3 hours. This computation time could be reduced if a faster PC is available.

Parameter			Value
PV array	@ 1000 W/m^2	$V_{\mathit{mpp}}$	611 V
		$I_{\mathit{mpp}}$	7.5 A
		$P_{\mathit{max}}$	4500 W
		$V_{\mathit{OC}}$	830 V
		$I_{\mathit{SC}}$	8.25 A
	@ 500 W/m^2	$V_{\mathit{mpp}}$	630 V
		$I_{\mathit{mpp}}$	4.2 A
		$P_{\mathit{max}}$	2400 W
		$V_{\mathit{OC}}$	780 V
		$I_{\mathit{SC}}$	4.25 A
QZSI		$L$	10 mH
		$C$	400 μF
Induction motor		Rated RMS $V_{L-L}$	460 V
		Rated frequency	60 Hz
		Rated power	4000w

Table 1.

System parameters’ values at rated power.

4.1 MPPT performance investigation

Figure 11 indicates the calculated PV performance parameters (voltage, current and power) with step change of duty ratio equals 1e-6. It is seen from the figure that the system can reach MPPT, even, at different insolation as recorded in the power curves. A good system components design leads to the fact that the rated PV panel power is larger than the rated power of the motor–pump system and battery charger power. The system shows that the solar panel is capable, at MPPT, to generate 4.5 kW at 1000 W/m² and 2.4 kW at 500 W/m². The perturb-and-observe controller suffers from a minor problem. The system tends to oscillate around the maximum power point, which is observed clearly in the power vs. time curve.

Figure 11.

PV power, voltage and current with P&O algorithm.

4.2 QZSI performance investigation

Figures 12 and 13 show QZSI modulation index variations and the change in the shoot-through duty ratio of the system. Rate of change in shoot-through duty ratio is increased rapidly by the step of change at the fifth second. The control technique keeps always the modulation index to be less than or equal to 1-D. This means that there is no overlapping between both controls. The increase of the irradiance of the system leads to increase in both the modulation index and the shoot-through duty ratio.

Figure 12.

Modulation index of the system.

Figure 13.

QZSI shoot-through duty ratio.

Voltages across capacitors C₁ and C₂ under different irradiance conditions are shown in Figure 14. Figure 15 records the inductor currents in L₁ and L₂. Voltage across capacitor C₁ is clamped to a level of around 838 V. This value includes voltage drop across the resistance of the battery (the battery voltage equals 775 V). Voltage across the capacitor C2 decreases by the decrease of the power. This can be explained depending on the fact that the output voltage is related to the motor power. It is seen that the inductor currents have always positive sign. Due to the existence of the battery, their patterns are not identical.

Figure 14.

Capacitor C₁ and C₂ voltages.

Figure 15.

L₁ and L₂ inductor currents.

4.3 Motor performance

Figure 16 shows motor line-line voltage and phase currents. Figure 17 shows the speed and power of the motor change with respect to changed irradiance; when the power and voltage increase, the speed correspondingly increases which fulfills the constant V/f control technique.

Figure 16.

(a) Motor voltage and (b) motor current.

Figure 17.

(a) Motor speed and (b) motor power.

4.4 Battery performance investigation

Figure 18 shows the battery performance parameters (state of charge, voltage and battery current). In the discharging mode, the battery state of charge decreases. The battery enters the charging mode and starts charging at the fifth second (when the irradiance increases). The SOC variation, between the two modes, is small. This is due to the short simulation period. The absence of the inductance in the battery current path causes the oscillation in the battery current. This is of course the cost of simple battery charging circuit design.

Figure 18.

Battery state of charge, current and voltage.

5. Conclusions

In this chapter, a PV-pumping system was developed. The design is based on battery-assisted quasi Z-source inverter. Traditionally, two-stage converter (boost converter followed by voltage source inverter) is employed in such applications. This work introduces a QZSI mathematical model. The proposed topology added a storage unit (battery). The position of the battery is selected to be shunted either with capacitor C₁ or with capacitor C₂.

In order to guarantee a good PV-pumping system performance, an overall control of the PV-pumping system with QZSI, assisted with a battery, is to be introduced. This algorithm of this controller should be able to force the PV panel to reach MPPT, even, under different conditions. Also, the battery must be allowed to enter the charging and discharging states in the proper timing and according to the system requirements. The inverter is controlled through the choice of the value of the modulation index as well as the shoot-through duty ratio. In order to prevent overlap between both control loops, the modulation index is designed to be less than or equal to (1-D) maximum allowable value. Consistency of simulation results with the analysis is an indication to the accurate system design steps. Simulation results, also, verify the proposed QZSI control technique. The system, under this control algorithm, provides continuous current in the inductors. This charging–discharging profile for the batteries satisfies a longer life time. The disadvantage is that the battery current is rich in ripples. This is cost of the simplicity design of the charging circuit [12].

Acknowledgments

The author appreciates the efforts introduced by Eng. Saad A. Altarfawi.