Modeling, analysis and design of efficient maximum power extraction method for solar PV system

Sustainable Energy Technologies and Assessments 15 (2016) 60–70

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Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta

Original Research Article

Modeling, analysis and design of efficient maximum power extraction method for solar PV system K. Sangeetha, T. Sudhakar Babu, N. Sudhakar, N. Rajasekar ⇑ School of Electrical Engineering, Solar Energy Research Cell, VIT University, Vellore 632014, India

a r t i c l e

i n f o

Article history: Received 4 August 2014 Revised 23 December 2015 Accepted 12 February 2016

Keywords: Solar photovoltaic system Efficient maximum power point tracking Voltage band method

a b s t r a c t A new method based on the concept of voltage band for efficient Distributed Maximum Power Point Tracking (DMPPT) of PV module is proposed. This novel formulation exhibits many advantages including faster convergence, improved tracking efficiency, zero steady state oscillations and simplicity in implementation. The paper unveils the possibility of utilizing a narrow voltage band for effective MPP tracking which has not been discussed so far in the literature. Extensive analysis is done and simulations are carried out in MATLAB/SIMULINK environment. To showcase the superiority of the proposed method, comparison is done with conventional methods for step change as well as gradual change in irradiation. Ó 2016 Elsevier Ltd. All rights reserved.

Introduction The global energy landscape is evolving at a fast pace due to dramatic economic growth and increase in population. As the energy demand goes uphill with each passing moment, the world is shifting focus towards research and utilization on alternative energy resources. Out of many renewable energy alternatives that have been explored in the recent past, solar energy is fast gaining popularity as it is clean, environment friendly and has less operational and maintenance costs. One of the major hurdles faced in implementing solar energy is its high installation cost. However, this is being slowly overridden by the recent technological advancements which have drastically lowered down the solar panel costs to a large extent. Once installed, solar energy can be harvested at nearly zero cost thus it proves to be a better costeffective solution in long run [1]. To harness maximum power from solar PV, Maximum Power Point Tracking (MPPT) methods are introduced. These techniques locate the unique operating point called Maximum Power Point via iterative procedure. However, occurrence of partial shading due to clouds, leaves, birds dropping etc. so PV array causes reduced power output. Further, under such conditions when centralized MPPT controllers are used it may get trapped in the neighborhood of relative maximum power point instead of absolute maximum power point [2,3]. Hence, to extract maximum power ⇑ Corresponding author. Tel.: +91 9952362301. E-mail addresses: [email protected] (K. Sangeetha), sudhakarbabu66@ gmail.com (T. Sudhakar Babu), [email protected] (N. Sudhakar), nrajasekar@ vit.ac.in, [email protected] (N. Rajasekar). http://dx.doi.org/10.1016/j.seta.2016.02.002 2213-1388/Ó 2016 Elsevier Ltd. All rights reserved.

it is advisable to employ Distributed MPPT (DMPPT) method [4–6]. Further, it has been demonstrated that performing MPPT on per-panel basis, instead of using a single MPPT controller can substantially increase the total harvested power; since each panel typically experiences distinct irradiation and temperature conditions [7,8]. While dealing with DMPPT, the MPPT method adopted should be simple, cost effective, minimal computations, fast convergence and zero steady state oscillations. From the literature it can be seen that many conventional MPPT methods like Constant voltage (CV) [9], Hill Climbing (HC) [10], Perturb and Observe (P&O) [11], Incremental Conductance (InC) etc. [12,13] have been devised for Distributed Maximum Power Point Tracking (DMPPT). In constant voltage method an approximate linear relation between Vmpp and Voc is followed. Although this method is lucid, the exact MPP cannot be tracked and it utterly fails when change in irradiation occurs [14]. Methods like HC follow a primitive approach to track MPP. It compares the present with previous power values and updates the duty cycle accordingly. However, this procedure is rendered ineffective in varying atmospheric conditions and its performance largely depends on the step size. To eradicate the above mentioned drawbacks, Incremental Conductance method was proposed and it is based on the fact that the slope of a P–V curve at Maximum Power Point is zero. Although InC is little more complex than HC, its MPP tracking efficiency is better. It tries to eliminate the steady state oscillations but it fails; since the null value of the slope of the PV array power versus voltage curve seldom occurs due to the resolution of digital controller [15]. Another interesting MPPT approach is Auto scaling variable step size MPPT method which considers the slope changes

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that occurs before and after MPP. The method is complex and it takes longer tracking time [16]. Geometric prediction of MPP by considering the P–V characteristics is another popular method to track the MPP accurately. This method is difficult to implement at the same time the usage of interpolation formulas adds to its complexity [17]. Besides these, several other fast converging MPPT methods have been evolved by introducing modifications to conventional methods [18–20]. In [18], a new algorithm based on the relationship between the load line and I–V curve of the PV module for faster MPPT response is proposed. Even though new equations are arrived to find the initial duty cycle values, approximating Vmpp, Impp values as constant does not hold good for all PV panels. Another modification for InC method is proposed in [19] to track GMPP under partial shaded condition and load variations as well. The algorithm follows complex procedure to find GMPP on PV curve and it uses conventional InC method to locate the 1st power peak attributing to poor response and large transient time. In [20] similar modification is incorporated to InC method so as to find MPP even under fast changing environmental conditions. The system is operated employing conventional InC method with new conditions coined to determine the direction of search process and its termination criteria. However, the disadvantages associated with conventional InC method are still prevalent. Apart from these, few other MPPT methods are also popular. This includes usage of window search algorithm to locate the global peak in string inverters [21]. In this work, voltage steps based on Power Operating Triangle (POT) restricts the voltage window to be scanned. However, this method requires complex computations due to continuous updation of POT. Another approach followed in [22], uses a linear control loop emulating a virtual load line for MPPT. The value of Vref is tuned iteratively either by P&O or Incremental Conductance method. The dynamic performance of the method is poor and it requires more number of iterations to reach MPP. Further, the accelerated performance via linear virtual load characteristics may not be true for all the panel characteristics; therefore, this method utterly fails when the MPP locus is not linear. Sliding mode control based MPPT is proposed in [23] where the findings are experimentally validated. But, the step size of 0.4 chosen in this work may result in significant power loss attributing to lower tracking efficiency and increases the probability of missing global optimum value. From the above discussion, it is understood that there is a need and scope for development of simple and efficient method for tracking MPP accurately. Hence, in this paper an attempt is made to formulate a new approach based on the concept of voltage band to yield better results. Voltage band is nothing but a range of voltage values where MPPs of all the irradiations lie. The proposed MPPT technique is suitable for Distributed Maximum Power Point Tracking with front end DC optimizer architecture with every PV module connected to DC–DC converter having individual MPPT control [24]. Application of this method restricts the search process and leads to faster MPP tracking. Further, when change in irradiation occurs the method proposed works fine since various combinations of temperature and irradiation have been taken into account while developing the proposed voltage band method. Under partial shaded condition, only the individual panel characteristics will be changed and it has already been taken into account while developing the proposed voltage band method. Furthermore, on application of voltage band method the dynamic performance is improved and steady state oscillations are completely eliminated. This method even works well under change in environmental conditions. The remaining portion of the paper is organized as follows. Section Solar PV modelling discusses the PV modelling of panel and Section Analysis of P–V characteristics is where analysis of P–V characteristics is done. Section Proposed voltage band method

provides an elaborate description about the proposed method. Section Overview of HC, InC and proposed VB method presents an overview of HC, InC and the proposed method. In Section Results and discussions simulation results taken with all the three methods obtained using MATLAB/SIMULINK are discussed. Section Conclusion expounds the conclusion. Solar PV modelling It is appreciable to build an effective PV model before proceeding to the installation part of the system so that it makes the design and testing much easier. It also helps in the better understanding of the behavior of a PV module under varying atmospheric conditions. Out of the various models proposed to emulate the PV module characteristics, single diode model is the most common. The model consists of a current source Ipv, a diode D, series resistance Rs and a shunt resistance Rp and it is shown in Fig. 1. Equations pertaining to single diode model are:

I ¼ Ipv  Id 


 Vd Rp

ð1Þ



 
 V þ IRs V þ IRs 1  I ¼ Ipv  Io exp aV t Rp

ð2Þ

The values of Ipv and Io can be computed analytically with the help of the following equations:




Ipv ¼ ðIscn þ K i  ðT  T n ÞÞ  Io ¼ h

exp



I pv



V ocn þkv ðTT n Þ aV t

1

G Gn



ð3Þ

i

ð4Þ

where Iscn = short circuit current at STC, Ki = current temperature coefficient, Tn = temperature at STC i.e. 25 °C, Gn = irradiation at STC i.e. 1000 W/m2, T = surface temperature of the module, G = irradiation in W/m2, Vocn = open circuit voltage at STC, Kv = voltage temperature coefficient, a = diode ideality constant, Vt = thermal voltage . which is given by V t ¼ ðNs kTÞ q From the aforementioned equations, it is evident that the computation of model parameters namely Rs, Rp and a is very essential to model the PV characteristics accurately. As they are not specified in the manufacturer’s datasheet, computation of these values has to be performed; either via analytical method or optimization technique. In this work, Bacterial Foraging Algorithm is used for the extraction of parameters and the values are Rs = 0.318671 O, Rp = 200 O and a = 1.2 [25]. Simulated I–V and P–V characteristics for the Kotak 80 W PV module obtained with extracted parameters are shown in Fig. 2. In order to confirm the accuracy of extracted parameter values experimental values are also embedded in the plot and it is seen that there exists a close agreement between the two. Rs

a

I

+

I01

Ipv

D1

Rp

V

-

Fig. 1. Equivalent circuit of Single diode model.

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Fig. 2. I–V and P–V characteristics of Kotak 80 W PV module.

Analysis of P–V characteristics A closer examination of the simulated P–V characteristics corresponding to different irradiations, shown in Fig. 2, reveal that power output of the PV module increases with PV voltage until it reaches the Maximum Power Point (MPP) there after it starts decreasing. The curve joining maximum power points of all possible irradiations is the actual MPP locus represented by a solid line in Fig. 2. It can be inferred from the figure that there is a considerable change in the maximum output power when change in irradiation occurs conversely with minimum variation in PV voltage. For better understanding of MPP locus and to know the existence of MPP locus for other panel, PV characteristics of four different panels having different voltage, current, power ratings and

make are studied. The simulated P–V characteristics of these panels along with their MPP loci are given in Fig. 3. From Fig. 3. it is explicitly clear from the P–V characteristics that MPP loci occurs for every panel and they are seems to be alike; irrespective of their make, type and power output. Further, it is noteworthy to mention that the occurrence of MPP voltages that corresponds to different irradiations lie within a limited PV voltage range; and it falls approximately in the range of 69–82% of Voc. To confirm with the above statement voltage the voltage band for all the above panels is computed and are tabulated in Table 1. This voltage range is named as voltage band (VB) in the present work. Further, to understand the effect of temperature change over the position of MPP in the PV characteristics is detailed. In order to demonstrate the suitability of the selected voltage band under

Fig. 3. P–V characteristics along with actual MPP loci for four different PV modules.

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where, Vmpn is the normalized MPP voltage at STC, Gn is the irradiation at STC i.e. 1000 W/m2, G is the irradiation in W/m2, b is the coefficient of the panel which varies with temperature and irradiation. For Kotak panel, b value is found to be 1.53.

Table 1 Voltage band obtained for four different PV modules. Panel name

Type of the panel

Obtained voltage band (expressed as % of V oc )

Shell Solar SP70 Shell Solar SM55 Shell Solar S36 KC200GT

Multi-crystalline Mono-crystalline Thin film Multi-crystalline

71.5–77.1 76.47–80.2 75.9–81.26 79.145–81.45

Overview of HC, InC and proposed VB method

various temperature conditions, extensive computations were done with different panels operating at various temperatures. From the computations made, conclusions arrived are presented in Table 2. From the tabulated values, it is clearly evident that the proposed voltage band lying in the range of 65–87% of Voc is capable of accommodating all the possible MPP that occur due to temperature changes. In practical situations, due to slight changes in atmospheric conditions, there exist small variations in voltage. In order to take this into account, a tolerance of 5% is considered on both sides of the obtained voltage band. Thus the voltage band limits set to 65–87% of Voc satisfies and accommodates both irradiation and temperature changes. From the above discussion, it is observed that the voltage band derived is quite narrow in comparison with the entire voltage span of the P–V curve. Since, the voltage band being very small, the search for MPP can be restricted within it rather than traversing the entire P–V curve. Moreover, the main shortcomings of conventional methods are (1) they fail to refine the search process in proper direction so that the methods. (2) Consume large number of steps to reach MPP and (3) exhibits significant steady state oscillations as well. Hence, application of voltage band (VB) method can straight away handle the above problems in the process of searching for Maximum Power Point. Proposed voltage band method From the detailed analysis done, it is evident that voltage band method could be effective in tracking MPP. However, before implementation, it is essential to compute the range of voltage limits within which all the MPPs lie. This section details the generalized procedure to be followed for finding the voltage band limits. The extreme limits of the voltage band are nothing but the Vmpp values at the maximum and minimum irradiations to which the PV module is exposed. The maximum irradiation that is incident on the PV module is 1000 W/m2 in most of the cases. The Vmpp corresponding to this irradiation is the voltage band upper limit and it is marked as VU in Figs. 7 and 8. Further, this value is readily available in the manufacturer’s datasheet. The lower extreme marked as VL is calculated using the following equation [26].





 G G þ ðkv  dTÞ  bV t log V L ¼ V mpn þ V t  ln Gn Gn

ð5Þ

An overview of existing MPPT methods namely HC, InC along with the proposed voltage band method is presented in the following section. Hill climbing algorithm The classical method used to track the Maximum power point is the HC method. This method is widely used due to its simplicity and any implementation [27,28]. In this method, the voltage and current values are sensed and based on previous and present power values the value of power, the duty cycle of the converter is adjusted [15,29]. The duty cycle is either incremented or decremented as to reach MPP value. Even though, this technique is lucid, easy to understand and implement. The major drawback of this method are increased oscillations near MPP fails to converge to MPP under shaded condition, and the time taken to reach steady state depends on the value of initial duty cycle and step size. The flowchart of the HC method is shown in Fig. 4. Incremental conductance algorithm As the name suggests, the ratio of the instantaneous current to instantaneous voltage (conductance) is used in this method. The duty cycle of the converter is varied according to the slope of the power to voltage characteristic. The duty cycle is increased by a step change whenever the slope of the curve becomes greater than a specified limit and is reduced whenever the slope becomes lower than the allowed value. Besides its complexity it tracks the maximum power point effectively under the conditions of uniform irradiation [25,28,30]. However, this method fails to reach steady state fastly and the converter duty cycle continues to oscillate around the MPP. The flowchart of this method is given in Fig. 5. Proposed VB method In this work, the search for MPP is based on the concept of a voltage band which has been elaborately discussed in Sections Analysis of P–V characteristics and Proposed voltage band method. From the above discussions it is clear that there exist a voltage band and by restricting the search process for MPP within this narrow voltage band (VB), MPP can be efficiently tracked. The procedure adopted for finding MPP using VB method is explained as follows. The search for MPP commences by sending three random initial duty cycles to the converter and the corresponding voltage, current and power values are recorded. To reduce the stress on the

Table 2 Variation in Vmp values under various temperature conditions. S.No.

Panel under study

1 2 3 4 5 6 7

S36 SP70 SM55 JAM6(R) KC200GT CS6-P TATABP250

Vmp values in % of Voc 5 °C

10 °C

20 °C

25 °C

82.502 78.8929 82.576 87.923 85.892

81.508 81.458 76.150 80.802

30 °C

40 °C

77.937 74.1729 78.74747

74.387 70.632 75.251 75.715

45 °C

50 °C

55 °C

76.894 74.676 77.898

60 °C

65 °C

70.286

64.270

72.038 73.898

67.186 72.254

70 °C

67.963 63.889 68.258

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Begin

Slope = 1

Sense Array’s Voltage V(k), Current I (k)

Calculate Power P(k) = V(k) * I(k)

P(k) > P(k-1)

No

Complement Slope

Yes

Duty cycle = Duty cycle + Slope * Constant Step Fig. 4. Flowchart of hill climbing algorithm.

checked. The two possible cases which may occur are (1) any of the random duty cycle lie inside the voltage band (2) none of the duty cycles lie inside the band. The proposed method is formulated taking into account both the probable conditions which are discussed in detail below. Case 1 – When one of the three voltages lies inside the voltage band. If any recorded voltage value lie within the defined Voltage Band, then the corresponding duty cycle say d2 is taken as new initial duty cycle dnew and the search process is continued by applying a small perturbation. This can be seen from Fig. 7. With this new duty cycle, a small perturbation Dd is either added or subtracted to find the new search direction. The search process continues till maximum power point is reached. Case 2 – When none of the voltages lie inside the voltage band. The following discussion is based on the assumption that none of the voltages that corresponds to the duty cycles d1, d2 and d3 lie inside the defined voltage band which is demonstrated in Fig. 8. In such a case, the duty cycle having close proximity with the voltage band should be adjusted in such a way that the duty cycle is pushed into the VB. To make this happen, the error voltages ei for the voltage values corresponding to all three duty cycles are computed.

ei ¼ V i  V m Begin

dV = V(k) - V(k-1) dI = I(k) - I(k-1) No

Yes No Change Yes Increase Duty cycle

dV = 0

dI/dV =- I/V

Yes

dI = 0 No

No dI/dV >- I/V No Decrese Duty cycle

ð6Þ ðV L þV U Þ , 2

Yes No Change

dI > 0

Yes

No Decrese Duty cycle

Increase Duty cycle

Update V(k-1) = V(k) I(k-1) = I(k)

Return Fig. 5. Flowchart of incremental conductance algorithm.

converter three duty cycles are used [31]. On the other hand, a minimum of three duty cycles are essential to trace the entire PV range. Hence, three duty cycles are chosen in this method. Since, the voltage band being known, the occurrence of any stored voltage value, that corresponds to duty cycle initialized, lying inside the band can be checked. The two possible cases which may occur are (1) any of the random duty cycle voltage lie inside the voltage band (2) none of the duty cycle voltage lie inside the band. Hence, these two cases are analyzed further and the respective flow chart is presented in Fig. 6. For highlighting the performance of the proposed voltage band method, critical analysis is carried out for all the random possible initializations. The search for MPP commences by sending three random initial duty cycles to the converter and the corresponding voltage values are stored. Since, the voltage band being known, the occurrence of any stored voltage value lying inside the band can be

where V m ¼ VL, VU are the lower and upper limits of the voltage band, Vm is the midpoint voltage of the band, ei is the error voltage for ith duty cycle value where i = 1, 2, 3, Vi is the operating voltage corresponding to ith duty cycle where i = 1, 2, 3. The duty cycle d corresponding to the least error voltage is the one closer to VB. Hence, this duty cycle is properly adjusted with a value Dd so that the resultant duty cycle dnew lies within the band. The value of Dd is chosen according to the magnitude of e. Once the voltage corresponding to duty cycle lies within the band, procedure mentioned in case 1 can be followed. Results and discussions To validate the effectiveness of the proposed method, PV module fed DC–DC boost converter is modeled in MATLAB/SIMULINK and simulations are carried out for different conditions. The SIMULINK model of the proposed system is shown in Fig. 9. The boost converter feeds a resistive load of 100 O and operates at a switching frequency of 10 kHz. The other converter components are L, C values and their designed values are 2.5 mH and 100 lF respectively. In this work, direct duty cycle control method is employed for MPP tracking and in effect the need for additional control loop is eliminated due to the inherent absolute MPP tracking capability. Further, it exhibits the following advantages (1) simple tracking structure (2) reduced convergence time (3) no tuning effort is required [32]. Dedicated MATLAB codes for all the three methods including the proposed method are written and their performances are studied. Extensive simulations are carried out in order to highlight the performance of Voltage Band method and the obtained results are compared with conventional and recent works to substantiate the findings. The irradiation pattern considered for performance tests of all the three algorithms is shown in the Fig. 10. Here, sudden and gradual changes in irradiation are modeled with the help of step and ramp inputs. Step change in irradiation On a sunny day, when cloud passes over PV module at a faster rate, there is a sudden increase or decrease in PV power output

K. Sangeetha et al. / Sustainable Energy Technologies and Assessments 15 (2016) 60–70

65

Start

Initialize three random Duty cycles d 1,d 2,d 3

Send Duty cycles to the converter and record corresponding Voltage and Current values

Any duty cycle voltage is within Voltage Band

Yes

D new = Voltage Band duty cycle i.e., any duty cycle with in d 1,d 2,d 3

No Update d new With Small perturbation

Compute error voltage ‘e’ select ‘d’ corresponding to least value of ‘e’

Update d new using Δd

No MPP reached Yes

No

If d new is within Voltage Band

Yes Maintain d new No Yes

If change in irradiation occurs

Fig. 6. Flow chart of the proposed voltage band (VB) method.

Fig. 7. P–V characteristics along with random duty cycles when it operates inside the band.

which further causes shift in MPP. Therefore, to evaluate the performance of the method under promptly changing environmental conditions, a step change in irradiation for an interval of 2 s is considered. The simulated response of all the methods (HC method, InC method, proposed VB method) when subjected to these conditions are illustrated in Figs. 11–13 respectively. Simulation results indicate that the time taken for MPP tracking for sudden change in environmental condition is 1.6 s and 1 s for HC and InC method respectively. However, VB method converges to MPP in just 0.5 s. This is because VB method limits the search process in a restricted voltage band thereby reducing the time

Fig. 8. P–V characteristics along with random duty cycles when it operates outside the band.

required to track MPP. Whenever a sudden change in irradiation is detected, the initialization is repeated and an operating point within the defined voltage band or closer to the band is obtained. This process ensures faster MPP tracking. When a step fall in irradiation occurs at time t = 4 s, all the algorithms try to track the MPP corresponding to the new irradiation say (200 W/m2). HC requires 0.95 s and InC needs 0.7 s for retracking; whereas VB method takes less than 0.25 s to locate the new MPP. It can be observed that alike HC algorithm, there exists a delay in MPP tracking for InC method when there is a step change in irradiation. In addition, both HC and InC methods exhibit steady

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Fig. 9. Matlab/Simulink model of MPPT controller and Boost converter.

Fig. 10. Irradiation pattern for algorithm testing.

Fig. 11. (a) Output voltage (b) output power (c) duty cycle waveforms for HC method.

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67

Fig. 12. (a) Output voltage (b) output power (c) duty cycle waveforms for InC method.

Fig. 13. (a) Output voltage (b) output power (c) duty cycle waveforms for VB method.

state power oscillations. The power ripple values are observed to be 6.3 W and 0.95 W respectively. However, this problem is absent in the proposed method as it nullifies the oscillations at steady state. Gradual change in irradiation Under normal circumstances, the irradiation keeps increasing gradually till noon afterwards it starts to fall. Such an atmospheric condition is quite common and using ramp signal gradual change in irradiation is realized for an interval of t = 6 s to t = 8 s and a decaying ramp from t = 10 s to t = 12 s. For the above time interval when gradual change in irradiation (ramp) occurs, it is observed that InC fails to track the power and it can be seen in Fig. 12. Once the irradiation stabilizes to a constant value (1000 W/m2), InC takes 1.2 s to arrive at the new MPP

whereas the time taken by HC is 0.4 s and that of VB method is 0.26 s. By observing the performance of InC method for the period from t = 6 s to t = 8 s, it can be concluded that it utterly fails to track the MPP. Hence InC method is undesirable when gradual irradiation change occurs. HC manages to track the power but it is not as effective compared to the proposed VB method. Once steady state is reached, HC and InC methods continue to oscillate around MPP which results in power losses. VB method guarantees better performance under gradual change in irradiation as compared to HC and InC methods. The inset images in Figs. 11–13 are the enlarged images of power ripple that persists at steady state. In addition, to demonstrate the supremacy of the proposed method over conventional methods, power values at every instant are compared with the ideal case and it is presented in Fig. 14. To scrutinize the concurrence between the desired and obtained

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are arrived based on sensed parameters, implementation complexity, transient power fluctuation, dynamic response, tracking speed, steps taken to reach MPP, steady state oscillations and tracking accuracy. From the Table 4 it can be inferred that the proposed VB method performs well in comparison with HC, InC and a fastconverging MPPT technique for photo voltaic system. One of the most important parameter governing the performance of MPPT method is its tracking efficiency defined as the ratio of obtained MPP value to that of the expected MPP value. After performing thorough simulations the computed tracking efficiency for all the methods is listed in Table 5. From the table, it is very much evident that the proposed VB method exhibits excellent tracking efficiency of 99.7% as it reaches a power value much closer to MPP compared to other conventional methods. Improvement in tracking efficiency is observed due to restricted search window and

powers for all the three methods, the expected and obtained power is plotted in the same graph. From Fig. 14, it can be deduced that VB method closely follows the desired power output according to the irradiation pattern applied whereas there is a noticeable variation in the actual and ideal power curves when HC and InC methods are used. VB method demonstrates superior performance at steady state with zero oscillations and has higher efficiency and improved performance compared to conventional methods. Table 3 summarizes the performance comparison of all three method in terms of power ripple and time taken for MPP tracking. From Table 3, it can be observed that VB method has the least power ripple throughout and it tracks the maximum power point fastly. Table 4 gives comparison between HC, InC, proposed VB method and fast converging MPPT technique [20]. The table values

Table 3 Performance comparison of HC, InC and proposed VB method. MPPT method

Initial tracking time (s)

Re-tracking time after sudden irradiation change (s)

Power ripple after sudden irradiation change (W)

Power ripple after gradual irradiation change (W)

HC InC VB

1.6 1 0.5

0.95–1.4 0.7–1.2 0.16–0.25

0.5–6.3 0.7–1.1 0.15–0.45

5.5–6.3 1–5.75 0.16–0.22

Fig. 14. Comparison of ideal and obtained power waveforms for HC, Inc and proposed VB method.

Table 4 Comparison between different methods.

*

Type

HC

InC

VB

A fast-converging MPPT technique for photovoltaic system [20]

Sensed parameters Implementation complexity Transient power fluctuation Dynamic response Tracking speed Steps taken to reach maximum power Steady state oscillations (Power) Tracking accuracy Re-tracking after step atmospheric change

V pv ; Ipv Very Low High Very Poor Very Slow 37 High Good >15 steps*

V pv ; Ipv Low Very High Very Poor Slow 36 High Good >15 steps*

V pv ; Ipv Low Low Good Fast 7 Zero Excellent <12 steps*

Vpv, Ipv High Low Good Fast 11 Zero Good <13 steps*

Depends on the irradiation change.

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K. Sangeetha et al. / Sustainable Energy Technologies and Assessments 15 (2016) 60–70 Table 5 Summary of MPPT Performance. Tracking methods

Irradiation (W/m2)

Simulation time instant (s)

Voltage (V)

Current (A)

Power (W)

Ideal power (W)

Tracking efficiency (%)

HC InC VB

1000 1000 1000

3.0736 3.0736 3.0736

16.2 16.18 17.18

4.80 4.811 4.68

77.8 77.85 80.45

80.7 80.7 80.7

96.40 96.46 99.7

minimized power oscillations. The additional feature that clearly distinguishes the proposed method from conventional one is duty cycle initialization and its convergence to optimum value. To support the sway of the proposed method, detailed analysis is made with respect to initialization, number of ticks, time taken to reach MPP, steady state performance and implementation complexity are presented in the following section. Initialization and number of ticks One of the major problems faced by conventional MPPT methods is the duty cycle initialization. The initial duty cycle is randomly initialised and is perturbed by a fixed step size. If the duty cycle corresponding to MPP (dmpp) lies far away from the initial duty cycle, the number of steps taken to reach MPP will be more which results in sluggish convergence [25,27,30,33]. However, this problem is solved in VB method since duty cycles are pushed into voltage band for faster convergence. Time taken to reach MPP The time taken to track MPP for conventional methods depend on the step size by which the duty cycle is adjusted. If the step size is small, the time taken to reach MPP will be more resulting in increased losses [24]. If the step size is more, time taken to reach steady state will be lowered whereas large fluctuations in power occurs at steady state which in turn reduces the tracking efficiency. This limitation deteriorates the performance of conventional methods. The proposed formulation tries to cover the entire P–V curve by sending three duty cycles to the converter. Once the duty cycle is pushed inside the voltage band, the method tracks MPP effectively with reduced time. The results prove that the proposed formulation tracks MPP swiftly compared to the conventional methods. Implementation complexity The proposed method is simple, easy to implement and does not involve complex mathematical computations. No trial and error method and complex iterative computations are required which adds to the fidelity of the formulation. It requires just a voltage and current sensor to track MPP accurately and effectively. The conventional MPPT methods are found easier to be implemented but they fail to provide sufficient class of accuracy. Conclusion In this work, an innovative MPPT method based on the concept of a voltage band (VB) is proposed. To highlight the improved Maximum Power Point Tracking capability of the new formulation, intensive simulation studies and analysis were performed for all the possible irradiation patterns. Further, the performance of the novel technique is critically compared with two classical MPPT algorithms HC and InC. The results prove that the proposed VB method outperforms HC and InC method in terms of convergence speed, tracking efficiency and steady state performance. In spite of all these advantages, it is very lucid to implement. The proposed

formulation can be used for Distributed Maximum Power Point Tracking for any PV module irrespective of its make, type and power rating. It is anticipated that this work will be beneficial for DMPPT and can draw significant attention of PV community.

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