Variable Step Size P&O MPPT Algorithm for PV Systems

Ahmad Al-Diab, Constantinos Sourkounis

Ruhr-University Bochum / Institute of Power System Technology and Power Mechatronics, Bochum, Germany. aldiab@eele.rub.de, sourkounis@eele.rub.de

Abstract—Maximum power point tracking (MPPT) techniques are employed in photovoltaic (PV) systems to maximize the PV array output power which depends on solar irradiance and temperature. Among all the MPPT strategies, The P&O Maximum Power Point Tracking algorithm is mostly used, due to its ease of implementation. On the other hand, its main drawbacks are the waste of energy in steady state conditions, when the working point moves across the MPP and the poor dynamic performances exhibited when a step change in solar irradiance or in temperature occurs. In this paper, a modified variable step size P&O MPPT algorithm is proposed, the step size is automatically tuned according to the operating point. Compared with the conventional fixed step size method, the proposed approach can effectively improve the MPPT speed and efficiency simultaneously.

A theoretical analysis and the design principle of the proposed algorithm are provided and its feasibility is also verified by simulation results.

I. INTRODUCTION

RENEWABLE energy sources are expected to play an essential role in the field of power production due to the increase of the world's power demand, of their independence from limited power sources and their low impact on the environment. Photovoltaic generation systems are currently considered to convert one of the most useful natural energy sources due to the continuous cost reduction, stable system, fast technological progress, being maintenance and pollution-free. They are used today in many applications such as battery charging, water pumping, home power supply, satellite power systems etc. The minimum element in PV systems is the PV module. Typical module is composed of series-connected solar cells, because of the insufficient power of one PV module is not enough. It is necessary to connect number of PV modules either in parallel or in series until the desired current and voltage levels are achieved.

Two existing drawbacks encountered while generating power from PV systems the first one that the efficiency of electric power generation is very low, especially under low radiation states, and the other drawback is the amount of electric power generated by solar arrays is always changing with weather conditions, i.e., irradiation and temperature.

Therefore a Maximum Power Point Tracking (MPPT) is an essential part of the PV system to ensure that inverters operate at the maximum power of the PV array. Several MPPT algorithms are developed, differing in concept,

complexity, number of the used sensors, cost and performance, in order to achieve a variety of aims including: accurate tracking, fast response speed and less oscillation due to the change of the solar irradiance and to the temperature. Among the popular tracking schemes are; the Perturb and Observe (P&O) or hill climbing, incremental conductance, fractional open-circuit current [1], and current sweep [1], and some modified techniques have also been proposed to achieve the mentioned objectives.

One of the most common MPPT technique [2] is to compare the PV array voltage (or current) with a constant reference voltage (or current), which corresponds to the PV voltage (or current) at the maximum power point, under specific operating conditions Fig. 1(a). The error signal is used to control a power conditioner which interfaces the PV array to the load. Although the implementation of this method is simple, but is not very accurate, since it does not take into account the effects of temperature and irradiation changing. Another MPPT technique is shown in Fig. 1(b), the PV array output current is compared with a reference current calculated using a microcontroller, which compares the PV output power before and after a change in the duty cycle of the power conditioner control signal. The PI controller regulates the PV output current to match the reference current.

This paper is presenting a modified P&O algorithm that is designed in order to overcome the drawbacks in traditional P&O MPPT algorithm. Varying the step size value reduces the oscillations around the MPP and leads to a faster response to reach it. When a step change in the solar irradiance occurs, the step size is automatically tuned according to the operating point. If the operating point is far from the MPP, it increases the step size which enables a fast tracking ability.

II. PV SYSTEM

Photovoltaic generates (DC) electrical power from semiconductors when they are illuminated by photons [14]. As long as light is shining on the solar cell, it generates electrical power. The most common solar cells technologies nowadays are the mono-crystalline, the poly-crystalline-silicon and Amorphous cells which are based on traditional, and expensive, semiconductor manufacturing processes. PV array consists of number of PV modules connected either in series or in parallel according to the required power

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On the other side, a PV module consists of a number of

connected solar cells in series, which are the basic element of any PV-System.

A. The Solar Cell A typical solar cell consists of a p-n junction formed in a

semiconductor material similar to a diode. It acts either as a voltage source or as a current source. The equivalent circuit of a solar cell is shown in Fig. 2. The photo-generated Current (IPh) is proportional to solar radiation. The maximum value of the solar cell output current (I) is the Short Circuit Current (ISC) which produced under short circuit conditions (V=0). While the maximum voltage at zero current, whereas the short circuit current is the maximum current at zero voltage, is called the Open Circuit Voltage (VOC).

The relationship between current and voltage may be determined from the diode characteristic equation:

Power (P) against voltage (V) characteristic curve of a PV module, Fig. 4, shows a unique point on the curve which the solar cell will generate maximum power. This is known as the maximum power point (Vmp, Imp), which depends on the solar irradiance and on the temperature.

Power Conditioner Load

Error Amplifier Comparator

Carrier Signal

Voltage or Current

PV Array

Power Conditioner Load

PV Power calculation and Iref

PI Control

PV Current

PV Array

PWM

Iref Error

Power Conditioner Load

PI Control

PV Voltage, Current

PV Array

PWM

0Error

dv/dI + I/VCalculations

(a) (b)

(c)

Reference Voltage or Current

Fig. 1. MPPT control systems. (a) MPPT control system with fixed voltage or current reference. (b) MPPT control system with current reference.

(c) MPPT system with the incremental conductance control method.

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Fig. 2. PV cell.

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Therefore; a MPPT is an essential part of PV system to ensure that inverters operate at the maximum power of the PV array.

B. The Perturb & Observe (P&O) Method The most commonly used MPPT algorithm is the (P&O),

due to its simplicity of implementation in its basic form. However, it has some drawbacks, like oscillations around the MPP in steady state operation, slow response speed due to the change of the solar irradiance.

P&O algorithm is based on the calculation of the PV array output power and the power change by sensing both the PV current and voltage. The tracker operates periodically by comparing the actual value of the power with the previous value to determine the change (incrementing or decrementing) on the solar array voltage or current (depending on the control strategy). If a given perturbation leads to an increase (decrease) in the output power of the PV, then the subsequent perturbation is generated in the same (opposite) direction [5, 9, 11, 18]. The algorithm is summarized in Fig. 4. When the MPP is reached, the system then oscillates around the MPP. In order to minimize the oscillation, the perturbation step size should be reduced. However, a smaller step size slows down the MPPT. A modified P&O algorithm is introduced in this paper in order to overcome this drawback by varying the step size that gets smaller towards the MPP and increases when the operating point is far from the MPP.

C. Modified Perturb & Observe (P&O) Method In general, MPPT algorithms use a fixed step size, which is

determined by the accuracy and tracking speed requirements. However, if the step size is increased for tracking speed-up, the accuracy is decreased, resulting in a comparatively low efficiency and vice versa. In this paper, a modified variable step size algorithm is proposed for the P&O MPPT method and is dedicated to find a simple, effective way to improve tracking accuracy and to overcome the drawbacks in traditional MPPT algorithms.

The flowchart of the modified variable step size P&O MPPT algorithm is shown in Fig. 5, where the step size is automatically tuned according to the PV array operating point. When a step change in the solar irradiance occurs, the step size is automatically tuned according to the operating point. If the operating point is far from the MPP, it increases the step size which enables a fast tracking ability.

In most applications, the MPPT is achieved by connecting a power conditioner (dc/dc or dc/ac converter) between the PV array and load. To simplify the control system the PV array operation point is employed to directly control the converter duty cycle based on a Phase Shift Pulse Width Modulation (PSPWM). The variable step size adopted to reduce the problem mentioned above is shown as follows: Where N is the scaling factor determines the performance of the MPPT system and is tuned at the design process. The MPPT control system is shown in Fig.7 which has an inherent characteristic as follows:

Fig. 4. Traditional Perturb & Observe (P&O) Method. Fig. 5. Modified Perturb & Observe (P&O) Method.

Voltage (V)

Pow

er (W

)Maximum Power Curve

1000 W/m2

600 W/m2

400 W/m2

200 W/m2

800 W/m2

Fig. 3. Change in power-voltage characteristics due to change of irradiance.

*( ) ( ) . (3)PD k D k NI

Δ= −Δ

0 PV operating point at the lift of the MPP.

0 PV operating point at MPP .

0 PV operating point at the right of the MPP.

PIPIPI

Δ >ΔΔ =ΔΔ <Δ

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On the first case when the value of , the step size should be increased which makes the magnitude of the phase shift to be produced will be decreased, therefore; the PV current flow through the high frequency inverter will be increased, causing an increase on the generated power. However, it will be the opposite for the third case. If the Array is running at the MPP, the value of , this keeps the value phase shift without any change.

D. Phase Shift Modulation Phase-shift PWM is based on the combination of square-

wave switching and PWM with unipolar voltage switching, it is used to regulate the output voltage by varying the relative phase shift of the two inverter legs in single-phase inverter [15, 16]. Both legs operate in square-wave mode, but the right-side leg operates at phase-shift angle δ.

The fundamental voltage can be controlled by the phase shift angle δ. The maximum fundamental voltage is obtained in square-wave mode when δ = 0° [13, 16]. Phase shift PWM has the advantage to get low switching and conduction losses compared to other PWM techniques at high switching frequencies.

III. SIMULATION EVALUATION

To verify the performance of the proposed modified variable step size P&O MPPT algorithm, a MATLAB-SIMULINK model of the PV system shown in Fig. 1 (b) is initially developed. Each PV string contains 12 modules, one module contains of 60 solar cells. The PV modules have the following manufacturing specification: Voc= 36.9V, Isc= 8.07A, voltage at maximum power= 30.2V, current at maximum power= 7.42A, taking in concern the deviations on the specifications due to the semiconductors manufacturing tolerances. To compare the performance of the variable step size P&O MPPT method with the common fixed step size P&O MPPT method, the simulations are configured under exactly the same conditions to compare the performances. The sampling period used for MPPT algorithm is chosen as 1ms. The duty cycle command is therefore updated every 1ms. The PV voltage, current and power of P&O MPPT with fixed step size of 0.01 and 0.1 under irradiation step change conditions are shown in Figs. 8-9. The irradiation was suddenly changed from 1000 to 200 W/m2 at 0.4 s and changed back to 1000 W/m2 at 0.8 s. While for a variable step size with N= 1.6.10-5, 1.10-4 the PV voltage, current and power are shown in Figs. 10-11.

Fig. 7. Block diagram of MPPT controller.

0PI

Δ >Δ

PI

ΔΔ

PI

ΔΔ

PI

ΔΔ

Fig. 6. (ΔP/ΔI) range on the PI-Curve.

0PI

Δ =Δ

Fig. 8. PV array output (a) voltage, (b) current, (c) power for fixed step size P&O MPPT equal to 0.01.

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The Energy yield for both fixed step size equals 0.01 and variable step with N= 1.10-5 the current sensor has 1% of the maximum PV current tolerance is presented in Fig.12.

Compared with the MPPT with fixed step size of 0.01, the MPPT with fixed step size of 0.1 shows a good dynamic performance but high steady state oscillations. The tracking time with fixed step size of 0.1 under irradiation step change conditions is only several MPPT sampling periods and the tracking ability can be further improved with larger step size. However, it is achieved at the sacrifice of MPPT efficiency. The PV array average output power with fixed step size of 0.1 decreased by 1.0% compared with the output power with variable step size of N= 1.10-6. The proposed variable step size method solves the drawbacks in traditional P&O MPPT. The oscillations at stead state in these two figures are almost half what is on the P&O MPPT.

The dynamic performance is faster than that of fixed step size. It also can be seen a bigger N can be chosen to achieve a faster response when a change in the solar irradiance occurs.

Fig. 9. PV array output (a) voltage, (b) current, (c) power for fixed step size P&O MPPT equal to 0.1.

Fig. 10. PV array output (a) voltage, (b) current, (c) power for variable step size P&O MPPT (N=1.10-5).

Fig. 11. PV array output (a) voltage, (b) current, (c) power for variable step size P&O MPPT (N=1.10-4).

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IV. CONCLUSIONS

In this paper, a modified variable step size P&O MPPT algorithm has been presented, which is able to improve the dynamic and steady state performance of the PV system simultaneously. The design issue of variable step size P&O MPPT is discussed and a simple design rule is proposed. Moreover, at the start process of the MPPT, the PV system may exhibit comparable large step change in the output voltage and current due to the large step size. Both fixed step size and the proposed variable size P&O MPPT methods are implemented with MATLAB- SIMULINK for simulation. The simulation results verify the feasibility and effectiveness of the proposed method

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200 400 600 800 1000

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Energy Yield Efficiency for Variable Step Size Energy Yield Efficiency for Fixed Step Size

Irradiance (W/m2)

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gy Y

ield

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cien

cy (%

)

Fig. 12. Energy Yield for fixed and variable P&O MPPT methods.

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