Research ArticleSimple Moving Voltage Average Incremental ConductanceMPPT Technique with Direct Control Method underNonuniform Solar Irradiance Conditions
Amjad Ali, Wuhua Li, and Xiangning He
College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Correspondence should be addressed to Amjad Ali; [email protected]
Received 8 October 2015; Accepted 1 December 2015
Academic Editor: Jegadesan Subbiah
Copyright Β© 2015 Amjad Ali et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A new simple moving voltage average (SMVA) technique with fixed step direct control incremental conductance method isintroduced to reduce solar photovoltaic voltage (πPV) oscillation under nonuniform solar irradiation conditions. To evaluate andvalidate the performance of the proposed SMVAmethod in comparison with the conventional fixed step direct control incrementalconductance method under extreme conditions, different scenarios were simulated. Simulation results show that in most casesSMVA gives better results with more stability as compared to traditional fixed step direct control INC with faster tracking systemalong with reduction in sustained oscillations and possesses fast steady state response and robustness. The steady state oscillationsare almost eliminated because of extremely small |ππ/ππ| around maximum power (MP), which verify that the proposed methodis suitable for standalone PV system under extreme weather conditions not only in terms of bus voltage stability but also in overallsystem efficiency.
1. Introduction
Penetration of solar photovoltaic (PV) power in centralizedor decentralized generation system has been evolving ata rapid pace in recent years and is considered to be oneof the most promising power generation options amongall renewable energy sources (RES) for sustainable energydevelopment. But due to the intermittency of environmentalconditions and nonuniform nature of solar irradiance itproduces significant fluctuation in solar power generation.This is because solar irradiance is not highly correlatedbetween even close locations at very short timescale which isone of the important factors in solar power generation outputvariability. Studies have shown that increased geographicaldiversity in solar PV generation system leads to decrease inthe output power efficiency and sometimes generates hot-spots which causes damage to the solar cells [1]. So farpower system operators accommodate solar and wind powervariability through storage reserves to stabilize the poweroutput levels [2]. Technically there are two ways to improvethe efficiency of PV power generation: it could be possible
either to develop low cost high efficiency solar conversionmaterials or to operate the PV system at maximum powerpoint (MPP) for getting optimal output power. Because ofthe high cost of solar cells, it is necessary to operate the PVarray at the maximum operating point. Therefore maximumpower point tracking (MPPT) is considered as an essentialpart of PV generation system and is one of the key issues forresearchers to reduce the effects of nonlinear characteristicsof PV array [3].
So far different MPPT algorithms have been proposedfor optimization of PV output power, such as perturb &observe (P&O) [4β6], incremental conductance (INC) [7, 8],hill climbing [9, 10], neural network, fuzzy logic theory, andgenetic algorithm [11β13]. However it has been observed thatmost of the MPPT methods are developed by assuming thatsolar irradiance is applied on the entire PV array uniformly.Unfortunately, the nonlinearity of solar irradiation is directlyeffecting the PV characteristic because of multiple localmaxima (the mismatching problem) which can be exhibitedon current-voltage (πΌπ curve) and power-voltage (ππ curve)
Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015, Article ID 479178, 12 pageshttp://dx.doi.org/10.1155/2015/479178
2 International Journal of Photoenergy
MPPTcontroller PI controller PV system
IPV IPVVPV VPV
VPV
Vref dβ+
(a)
MPPTcontroller PV system
IPV IPVVPV VPV
d
(b)
Figure 1: Block diagrams of INC MPPT algorithms implementation techniques; (a) reference voltage control; (b) direct duty ratio control.
of solar PV array if the entire array does not receive uniformsolar irradiation.
Although some researchers have worked on partiallyshaded condition (PSC) and fast changing solar irradianceMPPT [14β17], in [14], a two-stage MPPT with instant onlineπoc and πΌsc measurement was proposed. This MPPT is verysimple to implement but an additional circuit is required totrack the real maximum power point (RMPP) under nonuni-form insolation conditions; a novel algorithm to track theglobal power peak (GPP) under partially shaded conditionsbased on several critical observations in conjunction witha DC-DC converter to accelerate the tracking speed withfeed forward control is proposed in [15]. To ensure fastMPPT process with DC-DC converter duty cyclemodulationunder partial shading conditions and load variations withmodified incremental conductance (INC) algorithm to trackthe GMPP is proposed in [16] and a modified incrementalconductance algorithm under fast changing solar irradianceto reduce oscillation in solar module power at zero level andto mitigate the inaccurate response is discussed in [17].
Among all the aforementioned MPPT algorithms, incre-mental conductance (INC) and perturb & observe (P&O)are commonly used for small and large scale PV powerplants because both the algorithms operate in accordancewith power against voltage (π-π) curve of PV module andtune the duty cycle of converter to ensure the nextMPP pointaccordingly. In P&O steady state oscillation occurred becauseperturbation continuously changes in both the directionsto maintain MPP under rapidly changing solar irradiancewhich causes system to be less efficient and to have morepower losses [6, 18]. However, the conventional incrementalconductance method determines the slope of PV curve byvarying the converter duty cycle in fixed or variable step sizeuntil the MPP is achieved and in this way oscillation underrapidly changing solar irradiance is reduced with greaterefficiency but due to complicated algorithm speed is slow.
As discussed that nonlinear solar irradiance producessignificant fluctuation in PV output voltage (πPV). So far, noconsiderable work is done to minimize the fluctuations ofπPV terminal voltage of MPPT controller which is directlyrelated to optimizing the efficiency and reducing the MPPtracking time. In this paper a direct control incrementalconductance with simple moving voltage average (SMVA)technique is proposed. Using SMVA we examined the vari-ability of πPV among different PV array configurations withnonuniform solar irradiance to aggregate the plant outputat varying timescales. The simulation of proposed model isperformed in MATLAB/Simulink and results are providedwith comparison of conventional fixed step direct controlincremental conductance method. The comparison results
reveal that the proposed SMVA method provides betteroutput by eliminating the steady state oscillations and greateroutput which is fast and accurate with response to variationof solar irradiation.
In Section 2 of this paper an overview about conventionaland fixed step direct control INC is given and proposedSMVA technique is discussed in Section 3. Section 4 is aboutthe case example and in Section 5 results are discussed, andfinally in Section 6 conclusion is drawn.
2. Direct Control Incremental ConductanceMPPT Method
Traditional conventional incremental conductance INC isbased on two independent control loops as shown inFigure 1(a). The first loop uses the incremental and instan-taneous conductance to generate the error signal, and thesecond is the closed loop with a proportional- integral (PI)controller to drive the error to zero at MPP according to (1).But in practical implementation of INC under nonuniformsolar irradiance the slope of π-π characteristics curves(ππ/ππ = 0) at MPP.
Therefore, a direct control incremental conductancemethod is proposed in [19β21] to simplify the control circuit,in which second loop, the proportional-integral (PI) con-troller, is eliminated as shown in Figure 1(b), in which dutycycle is adjusted into the algorithm and, to recompense the PIcontroller error detection function, a small marginal error of0.002 is attuned in code. Now rewriting (1) of INC into directcontrol INC with fixed duty cycle and small marginal error,new equation comes out as (2):
ππΌ
ππ+πΌ
π= 0, (1)
ππΌ
ππ+πΌ
π= πIC. (2)
So, now INC equations can be rewritten as
ππΌ
ππ+πΌ
π= πIC β 0,
ππΌ
ππ+πΌ
π= πIC > 0,
ππΌ
ππ+πΌ
π= πIC < 0,
(3)
where πIC is reported as an error in incremental and instan-taneous conductance. The error (πIC) is set on constantbasis or by following trial-and-error procedure [22]. Butit has been observed that large marginal error provided
International Journal of Photoenergy 3
Irr. PV array DC/DCconverter
MPPTSMVA
Load
IPV
VPV
X(n)
Y(n)
Vref
DCBUSS
Figure 2: Proposed simple moving voltage average (SMVA) with incremental conductance MPPT connection.
faster convergence to MPP but produces unnecessary steadystate oscillations, whereas small marginal error produces lesssteady state oscillation with slow convergence which tends todecrease the efficiency of system [19].
3. Proposed Method
In this paper a simple moving voltage average (SMVA)technique is proposed for recovering oscillatory effect such asripple in solar PV generator voltage πPV under nonuniformsolar irradiance. The proposed technique is inspired byadvantages of practical simple moving average (SMA) modelwhich is frequently used in financial markets to form a trendfollowing indicator by reducing price fluctuations. Herein,SMVA does not predict price direction but rather definesthe voltage direction with a lag because it is based on solarirradiation to compute and average the irradiation signalin time series analysis. The moving average is a simplelow pass FIR (Finite Impulse Response) filter commonlyused for smoothing an array of sampled data/signal; so farSMA is effectively used by different scholars [22, 23] inengineering characteristic reducing noise in random sampleswhile retaining a sharp step response and computing themonitoring values to predict the future data.
Although several other soft computing methods havebeen developed, as we can find in the works of Stevensonand Porter [24], Hansun and Subanar [25β27], and Popoolaet al. [28, 29], moving average method is still consideredas the best method by many researchers due to its easiness,objectiveness, reliability, and usefulness.
Therefore, SMA technique is adopted for reducing theoscillatory effect of πPV under nonuniform solar irradiationconditions. The proposed simple moving voltage average(SMVA) model is developed by following (4) in conjunc-tion with fixed step direct control incremental conductanceMPPT as shown in Figure 2, where π(π) and π(π) are inputand output signal of the SMVA, respectively, and (π) is thesize of the moving average window, which holds the numberof samples of the input signal as per defined limit and operatesby averaging the number of points from the input signal toproduce each point in the output signal [30]:
π
β
πβ(πβ1)
π(π) =
πβ1
β
πβπ
π(π) β π (π β π) + π (π) ,
π (π) =1
π
π
β
πβ(πβ1)
π(π) .
(4)
A certain size of SMVA moving block diagram is shown inFigures 3(a) and 3(b), where (π) is moving along with thearray size compiled from the input signal, one element at atime, and the average of all elements in the current window isthe output of the SMVA. When calculating successive values,a new value comes into the sum and an old value drops out byreplacing each data point with the average of the neighboringdata points defined within the span. The proposed SMVAmodel flow chart in conjunction with INC is depicted inFigure 4.
The proposed SMVA model is computed by following
SMVA =ππ+0+ ππ+1+ β β β + π
π+πβ2+ ππ+πβ1
π. (5)
In technical analysis, the number of sample points π isstochastic. It depends on nonuniformity of solar irradianceone is concentrating on. One characteristic of the SMVAis that if the data have an intermittent fluctuation, thenapplying SMVA of that period will eliminate that variation(with the average always containing one complete cycle). If 20measurements,π
1throughπ
20, are available, the successive
5-period simple moving averages, for example, are as follows:
SMVA5=π1+π2+π3+π4+π5
5,
SMVA6=π2+π3+π4+π5+π6
5,
SMVA7=π3+π4+π5+π6+π7
5,
.
.
.
SMVA20=π16+π17+π18+π19+π20
5.
(6)
Technically it is not possible to compute a 5-period movingaverage until 5 periodsβ data are available.That is why the firstmoving average in the above example starts with SMVA
5.
In Figure 5 an output signal of SMA is given wherefluctuated (noisy) signal is smoothed by following (6), with10 and 20 data points, where it can be observed that as thefilter length increases (the parameter π) the smoothness ofthe output increases.
4 International Journal of Photoenergy
Output signalInput signal
x(n β 5)
x(n β 4)
x(n β 3)
x(n β 2)
x(n β 1)
x(n)
x(n + 1)
x(n + 2)
y(n β 5)
y(n β 4)
y(n β 3)
y(n β 2)
y(n β 1)
y(n)
y(n + 1)
y(n + 2)
1/N
+
+
+
+
(a)
1 2 3 N
Xy(n)
x(n)
1/N+
x(n β 3)x(n β 2)x(n β 1) x(n β (N β 2))
(b)
Figure 3: (a) Moving average circuit. (b) Block diagram ofπ-order simple moving average (SMA) circuit.
Table 1: Electrical characteristic data of Solkar 36W PV module.
Description RatingMaximum power (πmax) 37.08WpVoltage at maximum power (πmp) 16.56VCurrent at maximum power (πΌmp) 2.25 AOpen circuit voltage (πoc) 21.24VShort circuit current (πΌsc) 2.55 ATotal number of cells in series (π
π ) 36
Total number of cells in parallel (ππ) 1
4. Case Example
Roof top centralized PV system installed at Zhejiang Uni-versity, Yuquan Campus, College of Electrical EngineeringBuilding, is taken as an example as shown in Figure 6. In factthe installed PV system is regarded as a good one because ofthe same module and facing the sun in the same angle anddirection. Therefore irradiation of these panels is supposedto be uniform. However, one should notice the chiller, waterstorage tank, and weather data collection unit cause shadingeffects on adjacent panels as in red circles it can be seen.
With reference to ZJU roof top PV system, a 3KW systemwas designed by using a 37-watt PV module to quantifythe analysis; PV panel specifications are shown in Table 1.
Approximation is made such that the PV panel peak powerreduction rate is directly proportional to shading effects.Therefore, irradiance is estimated as (1) normal PV panel:1000W/m2 and (2) shaded PV panel between 768.36W/m2and 426.96W/m2 as shown in Figures 7(a) and 7(b).
According to Figures 7(a) and 7(b), arrays A, B, andC with different irradiance πΌπ-ππ characteristic curves aredrawn in Figure 8 in which multiple maximum power pointsdue to irradiance mismatch are observed.
5. Results and Discussions
To validate the performance of proposed simple movingvoltage average (SMVA) technique under nonuniform solarirradiation, a MATLAB/Simulink model was developed asshown in Figure 9, consisting of 3 KW PV array, a DC-DCboost converter (in Table 2 its component values are given),and a fixed step direct control incremental conductanceMPPT controller with the SMVA technique.
At the first step of the simulation, a nonuniform solarirradiation is applied to the PV array where irradiation wasset to 800W/m2 at π‘ = 0.0 s and decreased to 600W/m2 at0.02 s and increased back to 1000W/m2 at π‘ = 0.04 s; finallythe irradiation decreased from 800W/m2 to 600W/m2 from0.06 s to 0.1 s, with 25βC constant temperature. In traditional
International Journal of Photoenergy 5
No Yes
NoNo change No change
duty cycleduty cycle duty cycle duty cycle
No
Update
Return
Yes
Yes
No
No
Yes
Yes
Initialize SMVA
Clear X(n) and Y(n)
Compute SMVA
No
Yes
Start
= nSMV
A b
uffer
initi
aliz
ing
Yes
No
Get next value to buffer
Return
Calc
ulat
e ave
rage
Get
nex
t val
ue to
initi
aliz
e buff
er
Update
Divide with (N)
dV = V β VolddI = I β Iold
dV = 0
dI = 0dI/dV = βI/V
dI/dV > βI/V dI > 0
Vold = VIold = I
Clear Y(n) (avg. value)
Clear old buffer (n β 1)
(n + 1)
β n
nβ(n+1)X(k)
= n
Buffer size
Buffer size
Decrease DecreaseIncrease Increase
SMVA =Xi+0 + Xi+1 + Xi+(nβ2) + Xi+(nβ1)
n
+Β· Β· Β·
Figure 4: Flow chart of proposed simple moving voltage average (SMVA) model with direct control incremental conductance.
β5
0
5
Sample number
Am
plitu
de
β5
0
5
Am
plitu
de
β5
0
5
Am
plitu
de
0 10 20 30 40 50 60 70 80 90 100Sample number
0 10 20 30 40 50 60 70 80 90 100Sample number
0 10 20 30 40 50 60 70 80 90 100
(a) Original noisy signal (b) 10-point moving average (c) 20-point moving average
Figure 5: Example of a moving average filter. In (a), random noise signal. In (b) and (c), this signal is filtered with 10- and 20-point movingaverage filters buffer size.
6 International Journal of Photoenergy
Figure 6: Roof top PV system installed at ZJU.
Is_2Is_1 Is_3
βArray A Array B Array C
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
1000
W/m
2
IPV
VPV
+
β
(a)
Array A Array B Array C
768.
36
800
561.
23.2
1
426.
96
1000
W/m
2
1000
W/m
2
W/m
2
1000
W/m
2W
/m2
561.
23.2
1 W/m
2W
/m2
IPV
VPV
+
β
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
Pane
l_1
Pane
l_2
Pane
l_3
Pane
l_n
W/m
2
Is_2Is_1 Is_3
(b)
Figure 7: Centralized PV system. (a) Uniform solar irradiance. (b) Shaded system.
0
1
2
3
4
5
6
0 50 100 150 200 250
Array C Array B Array A
Voltage (V)
Curr
ent (
A)
Calculated at 1000 W/m2
(a)
Voltage (V)
0100200300400500600700800900
1000
0 50 100 150 200 250
Pow
er (W
)
Array C Array B Array A
Calculated at 1000 W/m2
(b)
Figure 8: (a) πΌπ characteristic curves, (b) ππ characteristic curves of PV array at 1000W/m2 and mismatch irradiance levels.
International Journal of Photoenergy 7
PV module
S
T
Proposed additional SMVA block
IGBT
g CE
Enable MPPTPWM
P
E
V
I
MPPT control
Irr.
T
L D
C R
MPPT parameters
IPV
VPV
VPVVavg
+V
βV
Figure 9: MATLAB/Simulink model of SMVAMPPT controller with DC-DC boost converter.
Table 2: Boost converter components values.
Component Value UnitCapacitor (πΆ) 93.75 uFInductor (πΏ) 1.66 mHResistor (π ) 53.3 OhmRated input voltage 200 VDCRated output voltage 400 VDCRated output power 3 KWMaximum average DC current 7.5 AmpsSwitching frequency 16 KHz
PV systems photovoltaic voltage πPV is directly given as aninput to MPPT controller but in the proposed model πPV isgiven as an input to the SMVAmodule as depicted in Figure 9,and output of SMVA is given as an input to MPPT controller.To investigate and validate the efficacy of the SMVA modelbuffer sizes (number of sample points) of π = 10 and π =30 with a change in duty cycle Ξπ = 0.001 are applied;simulation results are presented in Figure 10.
Figure 10(a) is an output voltage (πPV) of the PV arraywhich is given as an input to the SMVA module to performvoltage smoothing and reduce the fluctuation using a spanof data points following (6) with the buffer sizesπ = 10 andπ = 30. Figures 10(b) and 10(c) reveal the output comparisondifferences of fluctuated πPV and smoothed output of theproposed SMVA technique; Figures 10(d), 10(e), and 10(f) arezoomed from (a), (b), and (c) at π‘ = 0.05 to π‘ = 0.07 secondswhere differences can be easily observed between (d), (e), and
(f); results clearly indicate that the proposed method workseffectively to reduce the fluctuation and improve the stabilityof voltage. It is observed in Figures 10(e) and 10(f) that asmaller buffer size produces higher fluctuation; as the buffersize increases, the fluctuation decreases.
To demonstrate the effectiveness of the proposed SMVAmodel Figures 11(a), 11(b), and 11(c) show the variation ofthe duty cycle of fixed step direct control INC with Ξπ =0.001, 0.005, and 0.01 and stability of the proposed SMVAmodel, where π = 10 and 30. In Figure 11(a), fixed stepdirect control INC and the proposed SMVA duty cycles withdifferent Ξπ and π are depicted, whereas Figure 11(b) isexemplifying the maximum point (MP) tracking time (ππ),the fixed step INC reached MP at ππ = 0.008 seconds, andthe proposed SMVA model gained the same MP at ππ =0.0051 and ππ = 0.0058 seconds, respectively. Furthermore,Figure 11(c) is giving an idea about the stability of duty cycleat different Ξπ between INC and the proposed SMVA. Theresults clearly illustrate that performance of the proposedSMVA model is much better compared to the conventionalfixed step INC with all the three step sizes Ξπ = 0.001, 0.005,and 0.01 during steady and dynamic state conditions andoptimum duty cycle reached faster with less oscillation. Thedisadvantages of the fixed step INC with direct control areeliminated by the SMVA, in which the change in duty cycleΞπ became stable because of extremely small |ππ/ππ| aroundMP, according to the change in the error absolute valuebetween the instantaneous conductance and the incrementalconductance.
Furthermore, to inspect the effectiveness of the proposedtechnique under nonuniform solar irradiation, different
8 International Journal of Photoenergy
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1188190192194196198200202204206208
Vol
tage
(V)
Time (s)
VPV
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1188190192194196198200202204206208
Vol
tage
(V)
Time (s)
SMVA(N = 10)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1188190192194196198200202204206208
Vol
tage
(V)
Time (s)
SMVA(N = 30)
0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068 0.07192194196198200202204206208
Vol
tage
(V)
Time (s)
0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068 0.07192194196198200202204206208
Vol
tage
(V)
Time (s)
0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068 0.07192194196198200202204206208
Vol
tage
(V)
Time (s)
(a)
(b)
(c)
(d)
(e)
(f)
Figure 10: Simple moving voltage average filter. In (a) πPV, (b), and (c), this signal is filtered output πPV with SMVA, and (d), (e), and (f) arezoomed from (a), (b), and (c).
scenarios were simulated with a change in duty cycle Ξπ =0.001, 0.005, and 0.01 and the SMVA buffer size numberwas adjusted at π = 10. Results are shown in Figures 12and 13, where magenta color is representing the simple fixedstep direct control INCβs output voltage and power and bluelines are for the proposed SMVAoutputs. Results are showingthat performance of the proposed technique is much betterthan that of fixed step direct control incremental conductancemethod at different duty cycleΞπ step changes. It can be easilyobserved that the output voltage and power of the proposedtechnique give greater efficiency with more stability at allthe different step size changes as compared to direct controlINC, as it can be seen in Figures 12(a), 12(b), and 12(c) asΞπ increases from 0.001 to 0.01, and INCβs output voltagedecreases from the range of 385β407 volts to 374β397, wherethe upper limit decreases to 10 volts and the lower limit wentdown to 11 volts. In the SMVA output voltage remains higherthan the INCβs within the range of 387β410 volts to 385β405with the change in upper limit of 5 volts and lower limit to2 volts. In the same way, in Figures 13(a), 13(b), and 13(c)
output power comparisons between INC and the proposedSMVA method can be observed at Ξπ = 0.001, and INCβsoutput power is between 2775 and 3100 watts. At the sameduty cycle SMVA output power is 2825β3150 watts and atΞπ = 0.01 INCβs output power is 2625β2955, whereas SMVAoutput power is 2750β3055 watts.
Figures 12 and 13 show that the proposed simple movingvoltage average (SMVA) technique with direct control incre-mental conductance MPPT method can efficiently deal withthe tradeoff between dynamic response speed and steady stateaccuracy. The steady state oscillations are almost eliminatedbecause of extremely small |ππ/ππ| around MPP, as shownin Figure 10(f), the ripple voltage is less than 1.0 volt. Thedynamic performance is obviously better than that with fixedstep direct control INC.
Furthermore, Tables 3(a) and 3(b) surmise the measure-ment output voltage and power of INC and the proposedSMVA method with different buffer sizes π = 10, 30, and50 and change in duty cycle Ξπ = 0.001, 0.003, 0.005, and0.01 in order to verify the repeatability of the results, where
International Journal of Photoenergy 9
0 0.002 0.004 0.006 0.008 0.010.4
0.42
0.44
0.46
0.48
0.5
Fixed step INC with Ξd = 0.001Fixed step INC with Ξd = 0.005Fixed step INC with Ξd = 0.01
= 30= 10
Time (s)
Ξd
Proposed SMVA with NProposed SMVA with N
(a)
Fixed step INC with Ξd = 0.001Proposed SMVA with Ξd = 0.001, N= 30Proposed SMVA with Ξd = 0.001, N= 10
0.00510.0058 0.008
0 0.002 0.004 0.006 0.008 0.010.4
0.42
0.44
0.46
0.48
0.5
Time (s)
Ξd
(b)
Time (s)
Proposed SMVA Fixed step INC with Ξd = 0.001Fixed step INC with Ξd = 0.005Fixed step INC with Ξd = 0.01
7.5 8 8.5 9 9.5 10
Γ10β3
0.4
0.42
0.44
0.46
0.48
0.5
Ξd
(c)
Figure 11: Duty cycle: fixed step INC controller with Ξπ = 0.001, 0.005, and 0.01 and proposed method withπ = 10 and 30.
the same tests were carried out at three different irradiancelevels. It can be seen that, at Ξπ = 0.001, INC and SMVAperform extremely close in most cases because of smallchange in duty cycle, as it is reported in [31, 32] that smallerΞπ reduces the steady state losses caused by the oscillationof the PV operating point around the MPP, but it makes thealgorithm slower and less efficient in the case of rapid changein solar irradiation and larger step size contributes to fasterdynamics but excessive steady state oscillations, resulting ina comparatively low efficiency as it can easily be seen inFigures 12 and 13 and Tables 3(a) and 3(b) as change induty cycle increases from Ξπ = 0.001 to 0.01, INCβs outputvoltage and power decrease, and fluctuation increases. Fromthe above study, it is observed that in most cases SMVA givesbetter results with more stability as compared to traditionalfixed step direct control INC with faster tracking systemunder extreme weather conditions along with reduction in
sustained oscillations, which verify that the proposedmethodis suitable for standalone PV system under extreme weatherconditions not only in terms of bus voltage stability but alsoin overall system efficiency.
6. Conclusion
In this paper, simple moving voltage average (SMVA)technique with fixed step direct control incremental con-ductance method was employed. Simulation results showthat proposed technique is able to reduce πPV oscillations,thereby reducing the power losses faced by the conventionalINC algorithm under nonuniform solar irradiation. Alsothis method is able to improve not only the steady anddynamic state but also the design efficiency of system. Inconclusion the proposed method performs accurately and
10 International Journal of Photoenergy
INC
Time (s)
Vol
tage
(V)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1375380385390395400405410
Ξd = 0.001, N = 10
(a)
INC
Proposed SMVA
Time (s)
Vol
tage
(V)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1375380385390395400405410
Ξd = 0.005,N = 10
(b)
INC
Proposed SMVA
Time (s)
Vol
tage
(V)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1375380385390395400405410
Ξd = 0.01, N = 10
(c)
Figure 12: Output voltage comparison with Ξπ = 0.001, 0.005, and 0.01 andπ = 10.
Time (s) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
2600
2700
2800
2900
3000
3100
3200
Proposed SMVA
Pow
er (W
)
Ξd = 0.001, N = 10
(a)
Time (s) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
2600
2700
2800
2900
3000
3100
3200
Pow
er (W
)
INC
Proposed SMVA
Ξd = 0.005,N = 10
(b)
Time (s) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
2600
2700
2800
2900
3000
3100
3200
Pow
er (W
)
INC
Proposed SMVA
Ξd = 0.01, N = 10
(c)
Figure 13: Output power comparison with Ξπ = 0.001, 0.005, and 0.01 andπ = 10.
International Journal of Photoenergy 11
Table 3: (a) Output voltage comparisons between INC and SMVA at different Ξπ andπ. (b) Output power comparisons between INC andSMVA at different Ξπ andπ.
(a)
Ξπ
0.001 0.003 0.005 0.01INC SMVA (π =) INC SMVA (π =) INC SMVA (π =) INC SMVA (π =)
Irr. (W/m2) 10 30 50 10 30 50 10 30 50 10 30 50600 388.4 390.4 390.6 390.3 386.3 390.6 390.6 390.6 383.1 386.1 386.2 386.2 378.5 386.1 386.1 386.1800 396.8 398.5 398.7 399.1 394.8 399.0 399.0 399.0 391.5 394.7 394.6 394.6 386.7 394.6 394.6 394.61000 404.9 407.8 407.8 407.8 402.9 407.7 407.7 407.8 399.4 403.1 403.1 43.1 395.7 403.1 403.1 403.1
(b)
Ξπ
0.001 0.003 0.005 0.01INC SMVA (π =) INC SMVA (π =) INC SMVA (π =) INC SMVA (π =)
Irr. (W/m2) 10 30 50 10 30 50 10 30 50 10 30 50600 2827 2861 2861 2861 2798 2861 2861 2861 2751 2795 2795 2795 2687 2795 2795 2795800 2953 2986 2986 2986 2922 2988 2988 2988 2874 2919 2919 2919 2804 2919 2919 29191000 3081 3118 3118 3118 3039 3118 3118 3118 2992 3047 3047 3047 2931 3047 3047 3047
better than the conventional INC algorithm and simulationresults verify the feasibility and effectiveness of the proposedmethod.
Conflict of InterestsThe authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
This work is sponsored by the National Nature ScienceFoundations of China (51490682, 51377112) and the ZhejiangProvincial Natural Science Foundation (LR16E070001).
References
[1] J. Marcos, L. Marroyo, E. Lorenzo, D. Alvira, and E. Izco,βPower output fluctuations in large scale pv plants: one yearobservations with one second resolution and a derived analyticmodel,β Progress in Photovoltaics: Research andApplications, vol.19, no. 2, pp. 218β227, 2011.
[2] M. D. Tabone and D. S. Callaway, βModeling variability anduncertainty of photovoltaic generation: a hidden state spatialstatistical approach,β IEEE Transactions on Power Systems, vol.30, no. 6, pp. 2965β2973, 2015.
[3] E. Karatepe, Syafaruddin, and T. Hiyama, βSimple and high-efficiency photovoltaic system under non-uniform operatingconditions,β IET Renewable Power Generation, vol. 4, no. 4, pp.354β368, 2010.
[4] N. Femia, G. Petrone,G. Spagnuolo, andM.Vitelli, βA techniquefor improving P&OMPPT performances of double-stage grid-connected photovoltaic systems,β IEEE Transactions on Indus-trial Electronics, vol. 56, no. 11, pp. 4473β4482, 2009.
[5] N. Femia,D.Granozio, G. Petrone, G. Spagnuolo, andM.Vitelli,βPredictive & adaptive MPPT perturb and observe method,βIEEE Transactions on Aerospace and Electronic Systems, vol. 43,no. 3, pp. 934β950, 2007.
[6] A. K. Abdelsalam, A. M. Massoud, S. Ahmed, and P. N. Enjeti,βHigh-performance adaptive Perturb and observe MPPT tech-nique for photovoltaic-basedmicrogrids,β IEEE Transactions onPower Electronics, vol. 26, no. 4, pp. 1010β1021, 2011.
[7] F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, βA variable stepsize INCMPPT method for PV systems,β IEEE Transactions onIndustrial Electronics, vol. 55, no. 7, pp. 2622β2628, 2008.
[8] A. Safari and S.Mekhilef, βSimulation and hardware implemen-tation of incremental conductance MPPT with direct controlmethod using cuk converter,β IEEE Transactions on IndustrialElectronics, vol. 58, no. 4, pp. 1154β1161, 2011.
[9] S. Jain and V. Agarwal, βA new algorithm for rapid tracking ofapproximate maximum power point in photovoltaic systems,βIEEE Power Electronics Letters, vol. 2, no. 1, pp. 16β19, 2004.
[10] W. Xiao andW. G. Dunford, βA modified adaptive hill climbingMPPT method for photovoltaic power systems,β in Proceedingsof the 35th Annual Power Electronics Specialists Conference(PESC β04), vol. 3, pp. 1957β1963, IEEE, June 2004.
[11] A. Varnham, A. M. Al-Ibrahim, G. S. Virk, and D. Azzi, βSoft-computing model-based controllers for increased photovoltaicplant efficiencies,β IEEE Transactions on Energy Conversion, vol.22, no. 4, pp. 873β880, 2007.
[12] A. G. Abo-Khalil, D.-C. Lee, J.-K. Seok, J.-W. Choi, and H.-G.Kim, βMaximum power point tracking controller connectingPV system to grid,β Journal of Power Electronics, vol. 6, no. 3,2006.
[13] J. L. Agorreta, L. Reinaldos, R. Gonzalez, M. Borrega, J. Balda,and L. Marroyo, βFuzzy switching technique applied to PWMboost converter operating in mixed conduction mode for PVsystems,β IEEETransactions on Industrial Electronics, vol. 56, no.11, pp. 4363β4373, 2009.
12 International Journal of Photoenergy
[14] K. Kobayashi, I. Takano, and Y. Sawada, βA study on a twostage maximum power point tracking control of a photovoltaicsystem under partially shaded insolation conditions,β in Pro-ceedings of the IEEE Power Engineering Society General Meeting,vol. 4, p. 2617, Toronto, Canada, July 2003.
[15] H. Patel and V. Agarwal, βMaximum power point trackingscheme for PV systems operating under partially shaded con-ditions,β IEEE Transactions on Industrial Electronics, vol. 55, no.4, pp. 1689β1698, 2008.
[16] K. S. Tey and S. Mekhilef, βModified incremental conductancealgorithm for photovoltaic system under partial shading con-ditions and load variation,β IEEE Transactions on IndustrialElectronics, vol. 61, no. 10, pp. 5384β5392, 2014.
[17] K. S. Tey and S. Mekhilef, βModified incremental conductanceMPPT algorithm to mitigate inaccurate responses under fast-changing solar irradiation level,β Solar Energy, vol. 101, pp. 333β342, 2014.
[18] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, βOptimiza-tion of perturb and observe maximum power point trackingmethod,β IEEE Transactions on Power Electronics, vol. 20, no.4, pp. 963β973, 2005.
[19] T. Radjai, L. Rahmani, S. Mekhilef, and J. P. Gaubert, βImple-mentation of a modified incremental conductance MPPT algo-rithm with direct control based on a fuzzy duty cycle changeestimator using dSPACE,β Solar Energy, vol. 110, pp. 325β337,2014.
[20] A. Safari and S.Mekhilef, βSimulation and hardware implemen-tation of incremental conductance MPPT with direct controlmethod using cuk converter,β IEEE Transactions on IndustrialElectronics, vol. 58, no. 4, pp. 1154β1161, 2011.
[21] A. Safari and S. Mekhilef, βImplementation of incrementalconductance method with direct control,β in Proceedings of theIEEE Region 10 Conference (TENCON β11), pp. 944β948, Bali,Indonesia, November 2011.
[22] J. M. Hellerstein, W. Hong, S. Madden, and K. Stanek, βBeyondaverage: toward sophisticated sensing with queries,β in Infor-mation Processing in Sensor Networks: Second InternationalWorkshop, IPSN 2003, Palo Alto, CA, USA, April 22β23, 2003Proceedings, vol. 2634 of Lecture Notes in Computer Science, pp.63β79, Springer, Berlin, Germany, 2003.
[23] S. R. Jeffery, G. Alonso, M. J. Franklin, W. Hong, and J. Widom,βDeclarative support for sensor data cleaning,β in PervasiveComputing, vol. 3968 of Lecture Notes in Computer Science, pp.83β100, 2006.
[24] M. Stevenson and J. E. Porter, βFuzzy time series forecastingusing percentage change as the universe of discourse,β WorldAcademy of Science, Engineering and Technology, vol. 27, no. 55,pp. 154β157, 2009.
[25] S. Hansun, βPeramalan data IHSG menggunakan fuzzy timeseries,β Indonesian Journal of Computing and Cybernetic Sys-tems, vol. 6, no. 2, pp. 79β88, 2012.
[26] S. Hansun and Subanar, βPenerapan pendekatan baru metodefuzzy-wavelet dalam analisis data runtun waktu,β in ProsidingSeminar Nasional Ilmu Komputer (SEMINASIK) GAMA, pp.39β43, Yogyakarta, Indonesia, November 2011.
[27] S. Hansun, Penerapan pendekatan baru metode fuzzy-waveletdalam analisis data runtun waktu [Ph.D. thesis], Program StudiS2 Ilmu Komputer, FMIPA UGM, Yogyakarta, Indonesia, 2011.
[28] A. Popoola, S. Ahmad, andK.Ahmad, βA fuzzy-waveletmethodfor analyzing non-stationary time series,β in Proceedings ofthe 5th International Conference on Recent Advances in SoftComputing (RASC β04), pp. 231β236, Nottingham, UK, 2004.
[29] A. O. Popoola, Fuzzy-wavelet method for time series analysis[Dissertation], Department of Computing, School of Electron-ics andPhysical Sciences, University of Surrey, Surrey,UK, 2007.
[30] Y.Wang, K. Yang, C. He, and G. Chen, βA harmonic eliminationapproach based on moving average filter for cascaded DSTAT-COM,β in Proceedings of the 40th Annual Conference of the IEEEIndustrial Electronics Society (IECON β14), vol. 2, pp. 4508β4513,Dallas, Tex, USA, November 2014.
[31] L. Fangrui, D. Shanxu, L. Fei, L. Bangyin, and K. Yong, βAvariable step size INC MPPT method for PV systems,β IEEETransactions on Industrial Electronics, vol. 55, no. 7, pp. 2622β2628, 2008.
[32] N. H. A. Rahman, A. M. Omar, and E. H. M. Saat, βAmodification of variable step size INC MPPT in PV system,βin Proceedings of the 7th IEEE International Power Engineeringand Optimization Conference (PEOCO β13), pp. 340β345, IEEE,Langkawi, Malaysia, June 2013.
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