Performance Analysis of a Maximum Power Point Tracking Technique Using Silver Mean Method

The proposed paper presents a simple and particularly efficacious Maximum Power Point Tracking (MPPT) algorithm based on Silver Mean Method (SMM). This method operates by choosing a search interval from the P-V characteristics of the given solar array and converges to MPP of the Solar Photo-Voltaic (SPV) system by shrinking its interval. After achieving the maximum power, the algorithm stops shrinking and maintains constant voltage until the next interval is decided. The tracking capability efficiency and performance analysis of the proposed algorithm are validated by the simulation and experimental results with a 100 W solar panel for variable temperature and irradiance conditions. The results obtained confirm that even without any perturbation and observation process, the proposed method still outperforms the traditional perturb and observe (P&O) method by demonstrating far better steady state output, more accuracy and higher efficiency.


Introduction
SPV systems have the ability to convert solar power directly into electrical power.As solar energy is widely available and easily accessible, solar power generating systems are distinctly suitable as independent power supply.However, there are two major drawbacks of the SPV systems, the low energy conversion efficiency and high initial cost.The energy efficiency can be improved by tracking the maximum power from the sun irrespective of environmental conditions.Thus, maximum extraction of power is an enforced job that needs various methods to be adapted.Moreover, the output power of a PV panel is determined by the chief atmospheric factors such as the solar irradiance and the temperature.Hence, it is worth tracking maximum power from the PV system by introducing a new MPPT algorithm.
Various MPPT techniques have been proposed for Maximum Power Tracking (MPP) by using different control strategies.
Veerachary et al. [1] presented a converter based on PV cell voltage which has shown low ripple content and improved the array performance.But this method needs to detect the solar array power output and load power detection using the instantaneous voltage and current information, requiring voltage and current sensors.
Henry et al. [2] demonstrated a simple and elegant technique using SEPIC converter which can be used under a wide range of meteorological conditions.Salas et al. [3] implemented a new tracker based on PV current which yields better results.But when experimentally compared with conventional methods, it has shown to consume more computational time .Jancarle et al. [4] experimentally implemented a micro-controlled maximum power point tracker which improves the converter efficiency and reduces the electro-magnetic interference level.However, under the variable climatic conditions, the technique cannot operate efficiently.Karils et al. [5] implemented Fuzzy Cognitive Networks (FCN) to a PV system which has good per-formance during different irradiance and temperature conditions.Nonetheless, in fuzzy implementation, several parameters are selected on a trial and error basis, which mainly depends on designer experience and intuition.To overcome these disadvantages, a fuzzy neural network based MP point tracking is proposed.
Among the existing MPPT algorithms, the traditional P&O method is widely employed because of easy implementation and low cost.Nevertheless, P&O method requires much time to track the MPP, as it compares power before and after perturbation.Vast amount of oscillations are observed at MPP which reduces system efficiency.In order to overcome the demerits associated with the traditional method, a simple and efficient MPPT algorithm based on SMM is proposed in this paper, which chooses the search interval from the PV characteristic of the system.Efficiency and performance of the proposed algorithm are calculated and compared with that of the traditional P&O. Figure 1 depicts the basic prototype of the PV system which consists of an SPV array, a boost converter and the proposed MPPT controller connected to the load system.The voltage and current generated by SPV array are the inputs of the MPPT system, and the task of the MPPT algorithm is to track the maximum power irrespective of environmental conditions.The PV array and the DC-DC boost converter of the system are modeled and simulated using MATLAB/simulink.The rest of the paper is organized as follows: Sec. 2. and Sec. 3. depicts the PV cell mathematical modeling and the boost converter modelling, respectively.The proposed MPPT method is presented in Sec. 4. In Sec. 5. the performance analysis based on simula-tion and experimental results are given in detail, and Sec. 6. summarizes the conclusion.

PV Cell Mathematical Modeling
A solar cell is usually quite small, producing about 1 or 2 W of power, yet forming a basic building block of any SPV system.The PV cells have to be connected together in the form of large units, called modules, to boost the power output.The modules, in turn, can be connected to form larger units called arrays, which can be interconnected to produce more power.The output voltage can be increased by connecting the cells or modules in series, whereas the output current can be enhanced by connecting the cells or modules in parallel.The equivalent circuit of a PV cell is shown in Fig. 2, which consists of a current source (I ph ), a diode, a series resistance (R s ) and a parallel resistance (R sh ).The parallel resistance is infinite, and the series resistance is zero for an ideal PV cell.The output current of an ideal PV cell is given by the Eq. ( 1) and Eq. ( 2).
where I pv is the solar output current, I d is the solar diode current, I sh is the solar shunt current, I s is the saturation current, q is the electron charge (1.6 )), A is the diode ideality factor and T is the PV cell temperature (K).The PV cells are connected in series or parallel combinations to increase the output voltage or the output current [16].Let N s be the number of cells connected in series and N p the number of cells connected in parallel, then the output current of an ideal PV cell is given by the Eq. ( 3). ( The solar panel specifications for the proposed system are summarized in Tab. 1.The P-V and I-V curves  Fig. 3: P-V and I-V curves at variable irradiance and constant temperature of 25 • C.

Boost Converter Modeling
A DC-DC converter is employed to enhance the effectiveness of the PV system by equaling the voltage generated by PV array to the voltage required by the load.The input voltage of the converter is the solar module output voltage V pv that varies all the time.However, its output voltage V dc must be kept at a desired value.This is done by controlling the duty ratio, so that the operating point of the PV system can be adjusted to realize MPPT algorithm [17], [18] and [19].A boost converter is chosen to control the PV module's output voltage.The duty ratio 'D' of the boost converter is evaluated by employing the input-output relationship as shown in Eq. ( 4) [20], [21], [22] and [23].The equivalent circuit of the DC-DC boost converter is shown in Fig. 5, and the design parameters of the boost converter components specified in the proposed system are given in Tab. 2. The boost converter parameters are selected so that the performance of the proposed system is not deteriorated even under the low solar irradiance conditions. Tab.

Proposed Maximum Power Point Tracking Method
Due to low cost and simple implementation, P&O method is generally preferred for the tracking of maximum power from the solar panels.But the perturbation methodology involved in the tracker creates slow response and also generates oscillations after reaching MPP [24], [25] and [26].Hence, a classical technique based on silver mean is proposed in this paper for optimizing the functions.Silver mean of two quantities is defined as the ratio of the sum of the smaller and twice the larger of those quantities, to the larger quantity, which is the same as the ratio of the larger to the smaller quantity.Let a be the larger quantity and b the smaller quantity in a search area and let α S be the silver mean constant.Mathematically, it is expressed  by the following Eq.( 5), Eq. ( 6), Eq. ( 7) and Eq. ( 8).
The silver mean α S conjugate value is 0.41, which is obtained from the ratios of larger and smaller quantities.
Using the conjugate value, the optimization function is chosen from P-V curve as a closed interval are given in Eq. ( 9) and Eq.(10).
Corresponding powers at P (V 1 ) and P (V 2 ) are obtained from the PV system.By comparing the obtained powers, the interval shrinks either to The iterations are further continued until the condition V 2 −V 1 ≤ ε is satisfied.The algorithm for the proposed SMM based MPPT is shown in Fig. 6.This algorithm operates in a given interval and converges to MPP of the PV system by shrinking its interval.After achieving MPP, the proposed algorithm stops shrinking and maintains constant voltage until the next interval is decided.
The proposed MPPT controller can thus be used to track the maximum power.This algorithm has an advantage over P&O in that it can determine when the MPPT controller has reached the MPP, whereas P&O oscillates around the MPP.Also, this method can track the rapidly increasing and decreasing irradiance conditions with higher accuracy than P&O [27], [28], [29], [30] and [31].

Performance Analysis
Performance analysis of the proposed MPPT algorithm is carried out using simulated results in MAT-LAB/simulink and is compared with that of the traditional P&O.To validate the performance of SMM algorithm, experimental test is conducted considering the variations in irradiance and temperature.

Simulation Results
The performance of the proposed MPPT algorithm is analysed through simulation using the MAT-LAB/simulink environment.These results successfully validate the satisfactory performance of the proposed system even under varying weather conditions.The solar irradiance is varied dynamically from 1000 W•m −2 to 200 W•m −2 , as depicted in Fig. 7.The corresponding PV output power obtained for both the proposed and P&O schemes is shown in Fig. 8. Figure 8 shows many oscillations for traditional P&O for a fixed step of 1 V, where the proposed scheme shows better steady state and dynamic performance.A smooth drift is observed when there is a change in irradiance using the SMM method.The figures also show that the peak power tracked is in accordance with the variation of the solar irradiance.MPPT efficiency (η) is the main parameter which projects the effectiveness of the MPPT scheme.The performance analysis is obtained by calculating the MPPT efficiency (η) given by Eq. ( 11) for both the P&O technique and the proposed MPPT technique [32], [33], [34] and [35].
The obtained power is the maximum extracted power using either P&O or the proposed scheme, and the actual power is the theoretical maximum power provided by the basic PV model [36], [37] and [38].Table 3 and Fig. 9 show the PV output power using traditional P&O scheme for a fixed step of 1 V and 2 V and the proposed scheme for a change in irradiance from 200 W•m −2 to 1000 W•m −2 at a constant temperature of 25 • C. Table 4 and Fig. 10 show the PV output power using traditional P&O scheme for a fixed step of 1 V and 2 V and the proposed scheme for a change in temperature from 25 • C to 65 • C at a constant irradiance of 1000 W•m −2 .
Tab. 3: PV power obtained at different irradiance.The MPPT efficiencies using traditional P&O scheme for a fixed step of 1 V and 2 V and the proposed scheme for a change in irradiance from 200 W•m −2 to 1000 W•m −2 at a constant temperature from 25 • C are depicted in Tab. 5 and Fig. 11.The MPPT efficiencies for a change in temperature from 25 • C to 65 • C at a constant irradiance of 1000 W•m −2 using traditional P&O scheme for a fixed step of 1 V and 2 V and the proposed scheme are shown in Tab.6 and Fig. 11.From the simulated results, the proposed scheme shows top efficiency and superior performance compared to the traditional P&O scheme.Tab.4: PV power obtained at different temperatures.

Experimental Validation
A prototype MPPT system has been developed using the proposed method, as shown in Fig.  imental setup comprises an E4360 solar array simulator, which is connected to a boost converter [39], [40] and [41].The proposed algorithm is implemented using MSP430 (G2553) microcontroller, and the PWM signal generated by the controller is given to TLP250 optoisolator.Over all circuit voltage and current protection is supervised by 4027 and 4098 ICs.The switching frequency of converter is set to 25 kHz, and it is connected to a 50 Ω, 5 A resistive load.
To analyze the proposed scheme experimentally, the performance of the system for variable irradiance and   During variable irradiance testing, initially an irradiance of 800 W•m −2 is applied to the system and after a short duration irradiance is increased to 1000 W•m −2 .As the irradiance changes, there is a change in PV voltage, PV current and PV power of the PV system.From Fig. 14, it is observed that as the irradiance changes from 800 W•m −2 to 1000 W•m −2 , the PV current changes from 4.5 A to 5.01 A, the PV voltage changes from 14.25 V to 23.05 V, and PV power from 64 W to 100 W.
In order to validate the performance of PV system during variable temperature, experimental test is conducted at 25 • C and 35 • C temperatures.The PV current, voltage and power experimental results depicted in Fig. 15 show the robustness of the proposed MPPT method for changes in the temperature.From the P-V characteristics, it is evident that the change in temperature of the PV system is inversely proportional to the voltage and hence,there is a dip in system voltage and power as the temperature increases.From Fig. 15, it is observed that as the temperature changes from 25 • C to 35 • C, the PV current remains constant at 5.7 A whereas the PV voltage reduces from 18.1 V to 9 V and the PV power from 100 W to 51 W.
The performance comparison of the proposed method with the traditionally used P&O is shown in Tab. 7, and energy extracted per day and the revenue generated by selling the energy are presented in Tab. 8. From the results, it is evident that proposed SMM based MPPT method provides a very good dynamic performance.

Conclusion
A newly developed algorithm proposed in this paper has been able to track efficiently the maximum power of a solar array in a simple way.The simulation results, when implemented in MATLAB/Simulink for varying solar irradiance, showed maximum efficiency of 99 % even at 20 % of standard solar irradiance.Also, for varying temperature conditions, the maximum efficiency was observed to be significantly high.It's worth noting that even at high temperature of 65 • C, the high level of efficiency was maintained at 97 %.The annual energy extracted using the proposed method at 30 which is approximately 10 % more than that extracted from traditional P&O method.Thus, the test results demonstrate an outstanding effectiveness of the proposed method under varying solar irradiance and temperature conditions.Also, the system is found to be more efficient and simpler than the conventional P&O technique.
Furthermore, the robustness and feasibility of the proposed method, when validated by the experimental results for variable temperature and irradiance, exhibited superior performance with better MPP tracking and reduced oscillations during steady-state condition.

Tab. 1 :
PV panel specifications.and constant temperature of 25 • C is shown in Fig.3, and the P-V and I-V curves at different temperatures and constant irradiance of 1000 W•m −2 are shown in Fig.4.From Fig.
[a, b] which is equal to [0, V OC ].Since MPP of the PV system always stays close to the open interval, it can be further reduced from the left of the P-V curve.Initially, the two voltages V 1 and V 2 obtained in the interval [a, b]

Fig. 8 :
Fig. 8: Dynamic variation of PV power for P&O and proposed methods.
3, it is observed that with the increase in solar irradiance at constant ambient temperature, the current for the same voltage increases, and similarly, the maximum power also increases.The solar PV power increases nonlinearly with the increase in solar irradiance.From Fig.4, it is observed that for a constant solar irradiance, as the ambient temperature increases, both the maximum power and the open circuit voltage decreases.Hence,the best climate condition for a solar PV cell is high solar irradiation and low ambient temperature.
13.The exper- Tab. 7: Performance comparison of the proposed MPPT method.
Tab. 8: Energy extracted and revenue generated by selling the energy.
• C and 40 • C is 89012 kWh and 86596 kWh, respectively, MAHANKALI received his B.Tech degree in Electrical Engineering and the M.Tech degree in Instrumentation & Control systems from the Sri Venkateswara University College of Engineering, Tirupati, India, and the Ph.D. degree from Sri Venkateswara University College of Engineering, Tirupati, India.He is currently a Professor of Electrical Engineering in Sri Venkateswara College of Engineering and Technology, Tirupati, India.He published more than 70 research papers.So far, he has guided 9 Ph.D., and 38 M.Tech students.His research interests include electrical engineering, instrumentation & control systems and High Voltage Engineering.