A Novel PandOT-Neville ’ s Interpolation MPPT Scheme for Maximum PV System Energy Extraction

Photovoltaic (PV) system posses an optimal operating pointing, termed as Maximum Power Point (MPP). Using Maximum Power Point Tracking (MPPT) algorithm, MPP of PV system has to be tracked continuously in any climatic conditions. In general, traditional Perturb and Observe (PandOT) MPP tracker is widely used among existing controllers. But, PandOT fails to harvest maximum power from solar panel, in addition oscillations around MPP results in low efficiency of the PV system. The contradiction involved in the traditional controller can be addressed as PandOT operates with a fixed step size. Hence, with large step size MPP can be reached quickly but the magnitude of oscillations around MPP are high. Similarly, when PandOT operated with tiny step size magnitude of oscillations can be reduced at the same time PV system consumes much time to reach MPP. In order to eliminate the contradiction involved with traditional MPPT scheme and effectively optimize PV system energy, this paper put forwards a hybrid MPPT scheme based on PandOT and Neville interpolation. The proposed scheme is executed in two stages. In the first stage, PandOT is operated with a large step size till the voltage reaches near to maximum point. In the second stage, Neville interpolation is used to find the maximum power point. The performance of the proposed scheme is compared with Golden Section Search (GSS) and PandOT MPPT controllers. With the proposed scheme the convergence time required to reach MPP is improved greatly. Experimental prototype is designed and developed to verify the performance of the proposed scheme. Experimental and simulation results provide enough evidence to show superiority of the proposed scheme.


Introduction
Among renewable energy sources Photovoltaic (PV) power generation is marked as a remarkable one due to eco-friendly nature, low maintenance, absences of rotating parts.The non-linear characteristic of PV module has an optimal operating point and dependent on solar irradiance and temperature.Tracking optimal operating point in any conditions is the responsibility of Maximum Power Point Tracking (MPPT) scheme.Hence, MPPT algorithm plays a vital role in optimizing PV power.From literature many MPPT controllers (Ali et al. 2013) - (Trishan et al. 2007) such as Perturb and Observe (Dezso et al. 2013) Hill-climbing method (Karatepe et al. 2010), Incremental Conductance (Chia et al. 2011) method, Open Circuit Voltage (Andrea et al. 2015), Short Circuit Current (Xu Di et al. 2014), Incremental Resistance Method (Qiang et al. 2011), Ripple Correlation Control (Solodovnik et al. 2004), Slide Mode Control (Kim II-Song et al. 2006), Neural Network (Veerachary et al. 2003) and Genetic Algorithm (Slimane et al. 2014) have been proposed.
a Corresponding author: rathode.muralidhar@gmail.comTraditional Perturb and Observe (PandOT) MPPT controller operation is based on perturbing with a fixed step size (Baltas et al. 1986).Based on perturbation PandOT is categorized into three types as, (i) Voltage based PandOT (Carannante et al. 2009) (ii) Current based PandOT (Abdelsalam et al. 2011) and (iii) direct duty ratio based PandOT (Sera D et al. 2008).Among existing controllers Perturb and Observe/ Hill Climbing methods are widely used in industrial and public sectors due to low cost and simple implementation (Alajmi et al. 2011).The minor difference between PandOT and Hill Climbing Method (HCM) is presented in (Eltawil et al. 2013), as HCM operation is based only on duty ratio.Apart from this, the major demerits associated with PandOT are slow response, confuses to decide optimal operating point of the PV system and oscillations in output power reduces efficiency (Subudhi et al. 2013).
The authors of (Xiao et al. 2006) - (Femia et al. 2008) have presented different strategies to improve the performances of PandOT.In (Emilio et al. 2014), a simple two step algorithm is attached with PandOT for better efficiency.A modified PandOT is proposed in (Killi et al. 2015), to avoid drift in output power of the PV system.In (Kota et al. 2016), the performance of PandOT is enhanced by estimating a voltage point near to the optimal operating point.
For standalone PV system, Incremental Conductance (INC) based MPPT scheme is generally preferred (Liu et al. 2008) due to drift free power generation during varying atmospheric conditions (Safari et al. 2011).Fractional Open Circuit Voltage (Adly et al. 2011) and Fractional Short Circuit Current methods (Masoum et al. 2002) are combined with other MPPT schemes to improve time response, steady state and dynamic performances of the PV system (Hart et al. 1984).Ripple Correlation (Casadci et al. 2006) and Slide Mode Controllers (de Brito et al. 2011) have successfully eliminated the drawbacks associated with traditional MPPT schemes.At the same time, fails to achieve Maximum Power Point (MPP) quickly during dynamic weather conditions (Koutroulis et al. 2001).
Hence, to avoid the demerits allied with existing MPPT methods, this paper put forwards a novel MPPT scheme combing PandOT with Neville Interpolation.The proposed scheme is executed in two stages.In the first stage, PandOT is operated with a large step size such that PV system converges quickly to the region of operating point.As it is well known that, PandOT oscillates around MPP with respect to step size provided initially to operate.The magnitude of oscillations clearly depends on the step size.In the second stage, three voltage points are chosen from the region around MPP and given as input for Neville Interpolation.Among these three voltage points, the Neville polynomial equations settle down to the exact MPP of PV system.Until there is a change in irradiance or temperature, MPP of PV system is maintained as constant.The contradiction involved in the traditional controller is eliminated with Neville Interpolation.The proposed scheme is compared with PandOT and GSS MPPT controllers.The test results provide enough evidence to prove superiority of the proposed scheme.
This paper is organized as follows: after brief introduction on traditional MPPT scheme drawbacks, mathematical modeling of PV cell is presented in Section 2. Proposed scheme along with PandOT and GSS controllers are presented in Section 3. Simulation results under real environmental conditions are presented in Section 4. Designed prototype with experimental results is presented in Section 5.And section 6 concludes the paper.

Mathematical Modeling of PV cell
The electrical equivalent circuit of a single diode Photovoltaic (PV) cell is shown in Fig. 1.PV cell is a combination of p-type and n-type semiconductor materials.When solar irradiance or equivalent energetic light is focused on PV module, free electrons are diffused to generate electric energy.Typically, PV cell posses low voltage hence PV cells are connected in series or parallel combination to meet the load rating.A simplified I-V characteristic equation is used in this paper to determine output current of PV cell and mathematically expressed as follows (Venkata et al. 2016) The two coefficients 'α1' and 'α2' are described as (2) where VM, IM, VOC and ISC are given by equations ( 4) -( 7) where: T is temperature on the panel surface (°C), TSTC is temperature at STC (25°C).The nonlinear I-V and P-V characteristics of RNG-100D 100Watt mono-crystalline PV panel at different irradiance and temperatures is shown in Fig. 2 and corresponding PV panel specifications are presented in Table 1.

Dc-dc SEPIC Converter
The electrical equivalent circuit of a dc-dc Single Ended Primary Inductor Converter (SEPIC) is shown in Fig. 3.The converter has the capability to step-up or step-down the supply voltage.The converter is employed with filter capacitor (Cf), inductor (L1, L2), capacitors (C1, C2), MOSFET (M) as switching operator and Diode (D) (Killi et al. 2015). Operation where 'D' is duty cycle, VPV is panel voltage and VLoad is output voltage of the converter.SEPIC converter parameters used in this paper is illustrated in Table 2.   Therefore, it is worth to conclude that closed interval initial selected [0, VOC] is reduced at each iteration until |V2-V1| ≤ ԑ is achieved.In normal conditions, GSS gives acceptable performance but fails to cope MPP under real environmental conditions.Flowchart of the GSS MPPT scheme is shown in Fig. 5. (f) At every change in irradiance and temperature closed interval has to be updated.

Proposed scheme
From literature, the contradiction involved in PandOT is addressed as PV system perturbed with large step size reaches MPP quickly but the magnitudes of oscillations around MPP are high.At the same time, tiny step size impacts the magnitude of oscillations effectively but consumes much time to reach necessary operating point as shown in Fig. 6.
In order to eliminate the contradictions associated with traditional perturb and observe controller, this paper presents a novel MPPT scheme based on PandOT and Neville Interpolation.The proposed scheme is executed in two stages.

Stage I:
Initially, PV system is operated with traditional PandOT controller with a large step size of 4 Volts to achieve MPP region within a precise time.After approaching MPP region, traditional controller oscillates in both forward and reverse directions around MPP.At that instant three voltage points are noted as shown in Fig. 7.These three voltage points are chosen as input for the second stage.

Stage II:
For better convenience these three voltage points are simplified as

Yes
In the second stage, these three voltage points are chosen as the inputs for Neville Interpolation.And the intermediate steps involved in the proposal are depicted in Fig. 9.   ( ) Finally, the Neville Interpolation polynomials in terms of intermediate is as follows ( ) Therefore Eq. ( 15) can be simplified as The polynomial equations settle down the sampling points to exact MPP of PV system.After achieving VMPP from Neville Interpolation, PV system duty cycle is maintained constant until there is a change in irradiance or temperature on the panel surface.A simple comparison between PandOT operated with 4V step size and proposed scheme is presented in Fig. 10.Error correcting loop helps to cope with actual power locus during change in irradiance and temperature.After acheving maximum power, the proposed scheme is perturbed around MPP with a small step size of 0.1V i.e. δV.
The flow chart depicted in Fig. 11 clearly summaries the working of the proposed MPPT scheme.The proposed scheme is simple and easy to implement.In addition achieves MPP with in a precise time and avoids the drawbacks associated with PandOT and GSS.A 3-Dimensional view of MPP obtained from the proposed Neville Interpolation scheme at different irradiance and temperatures levels is plotted in Fig. 12.

Initially,
MPPT schemes are developed in MATLAB/SIMULINK.Simulating at a particular irradiance or temperature value doesn't project effective working of any MPPT scheme.Hence, in this paper MPPT schemes are simulated under real environmental conditions.Using CS300-L silicon cell pyranometer, every change in irradiance and temperature are noted for a duration of eight hours as plotted in Fig. 13 (a) and (b).Initially, the irradiance profile shown in Fig. 13(a) is started with a minimum irradiance of 138.131W/m 2 at a temperature of 27.606°C.After a time period of 0.145 Sec the profile experiences a maximum irradiance of 729.906W/m 2 with a temperature of 32.731°C.During the testing period temperature on PV system is observed in between 27.5°C to 34°C as shown in Fig. 13(b).Fig. 14 shows PV system output current using different MPPT schemes.From P-V and I-V characteristics in Fig. 3, it can be concluded that irradiance on the panel surface is directly proportional to PV current.Hence, change in irradiance effects the shape of PV current.From figure, it is clearly visible that magnitude of oscillations in PandOT are very high, on the other hand GSS fail to track the current locus path perfectly.While, the proposed MPPT scheme tracks the locus path perfectly without any oscillations.Similarly, PV system output voltage and power are illustrated in Fig. 15 and 16.It is worth to conclude the analysis of the simulation test as the proposed MPPT scheme harvests maximum power from PV system compared to GSS and PandOT.During low irradiance level GSS fail to optimize power locus, whereas PandOT tracks the locus with oscillations.A detailed comparison of MPPT schemes under real environmental conditions is depicted in Table 3.At the same time efficiency are plotted in Fig. 17

Experimental Validation
To validate the performance of the proposed MPPT scheme a prototype is designed and developed.PV system parameters used for simulation and experimentation are same as depicted in Table 1 and 2. The solar panel is connected to SEPIC converter through Hall effect LA25-P current sensor and 7840 IC based voltage sensing circuit.The proposed scheme is programmed in DSP 30F4011 microcontroller and obtained pulses are given to 4081IC based PWM generator.In order to reduce losses between sensors and microcontroller TL084 buffer IC is employed.From PWM IC gate pulses are driven to switching device.Overall voltage and current protection is supervised by 4027 and 4098 flip-flop IC circuit.
Steady state performance of the proposed scheme is shown in Fig. 18.During this test PV system experiences an irradiance and temperature of 298 W/m2 and 28.5°C.For this particular irradiance and temperature values PV system has the capability to deliver a maximum power of 28Watt, with a maximum current and voltage of 1.5A and 17 V.The proposed scheme is succeeded in extracting maximum current, voltage and power at steady state performance.
The performance of the proposed scheme during raise in irradiance is plotted in Fig. 19.Initially, irradiance and temperature on the panel surface are increased from G=620 W/m2 and T=33.1°C to G=660W/m2 and T=32.8°C.The proposed scheme has a quick response in its output power.At, G=620 W/m2 and T=33.1°CPV system output parameters are PMax=60W, VMax=17.7V and IMax=3.2A.Correspondingly, at G=660W/m2 and T=32.8°C,PV system parameters are PMax=70W, VMax=18V and IMax=3.5A.from Fig. 19, it is clearly noticeable that the proposed scheme tracks maximum power path perfectly during change in irradiance.Similarly, Fig. 20 shows the performance of the proposed scheme during decrease in irradiance.At this test temperature on the panel is approximately same i.e., T=33°C and irradiance is changed from 390W/m2 to 335W/m2.From the experimental results it is evident that the proposed scheme harvest at most power from PV system in any weather conditions.In Table 4, performance of the proposed scheme is compared with PandOT and GSS controllers.

Conclusion
This paper put forwards a novel MPPT scheme combing PandOT and Neville Interpolation to optimize steady state performance of the traditional controller, which is far superior to PandOT and GSS.The proposed scheme is executed in two stages.In the first stage, MPP region is reached using PandOT with a large step size of 4V.And in the second stage, exact MPP is attained by Neville Interpolation.Hence, the proposed scheme has improved steady state performance of the PandOT controller effectively.From the simulation and experimental results, it is evident that the proposed scheme is far superior to the traditional PandO and GSS MPPT controllers.

Fig. 1
Fig. 1 Single Diode PV Cell Non-linear P-V and I-V characteristics at different (a)-(b)irradiance and (c)-(d)temperatures

Fig. 4
Fig. 4 Traditional Perturb and Observe Controller Flowchart4.2 Golden Section Search (GSS)In(Kheldoun et al. 2016), presented a novel MPPT scheme based on Golden Ratio.At first, based on PV system open circuit voltage a closed interval [0, VOC] is selected.And thereafter, two voltage points V1 and V2 are generated in the closed interval as (a) Based on open circuit voltage, select closed interval [0, VOC] (b) From Eq. (10), two voltage points are generated in the closed interval (c) Powers at voltage V1 and V2 are compared to decide next interval.If P(V1) > P(V2), the closed interval is updated as [0, V2] or else [V1, VOC] (d) Again, from (a) to (c) procedure is repeated (e) Once the condition, |V2-V1| ≤ ԑ is attained.The procedure converged to MPP.

Fig. 7
Fig. 7 At MPP, perturbation in forward and reverse directions.

Fig. 10
Fig. 10 Comparison between PandO and proposed scheme

Fig
Fig. 12 3-Dimensional view of voltages obtained using the proposed MPPT scheme .

Fig. 14 Fig
Fig. 14 Output current of PV system Efficiency (a) PandO (b) GSS and (c) Proposed scheme(c)

Fig. 18
Fig. 18 Steady state performance of the proposed scheme

Table 1
RNG-100D PV panel specifications of the converter is separated into two as Continuous Conduction Mode and Discontinuous Conduction Mode.If the current passing through inductor L1 is equal to zero, converter is operating in Discontinuous Conduction Mode.During Continuous Conduction Mode of operation, inductor L1 is always greater than zero.For a duty cycle more than 50%, converter boosts the supply voltage and vice versa if the duty cycle is less than 50%.Duty cycle of the converter is given as Performance comparison of the proposed MPPT scheme