# Simple Moving Voltage Average Incremental Conductance MPPT Technique with Direct Control Method under Nonuniform Solar Irradiance Conditions

Authors: Amjad Ali; Wuhua Li; Xiangning He
Journal: International Journal of Photoenergy
 (2015)

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## Abstract

A new simple moving voltage average (SMVA) technique with fixed step direct control incremental conductance method is introduced to reduce solar photovoltaic voltage (V
P
V) oscillation under nonuniform solar irradiation conditions. To evaluate and validate the performance of the proposed SMVA method in comparison with the conventional fixed step direct control incremental conductance method under extreme conditions, different scenarios were simulated. Simulation results show that in most cases SMVA gives better results with more stability as compared to traditional fixed step direct control INC with faster tracking system along with reduction in sustained oscillations and possesses fast steady state response and robustness. The steady state oscillations are almost eliminated because of extremely small d
P
/
d
V around maximum power (MP), which verify that the proposed method is suitable for standalone PV system under extreme weather conditions not only in terms of bus voltage stability but also in overall system efficiency.


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## Body

## 1. Introduction

Penetration of solar photovoltaic (PV) power in centralized or decentralized generation system has been evolving at a rapid pace in recent years and is considered to be one of the most promising power generation options among all renewable energy sources (RES) for sustainable energy development. But due to the intermittency of environmental conditions and nonuniform nature of solar irradiance it produces significant fluctuation in solar power generation. This is because solar irradiance is not highly correlated between even close locations at very short timescale which is one of the important factors in solar power generation output variability. Studies have shown that increased geographical diversity in solar PV generation system leads to decrease in the output power efficiency and sometimes generates hot-spots which causes damage to the solar cells [1]. So far power system operators accommodate solar and wind power variability through storage reserves to stabilize the power output levels [2]. Technically there are two ways to improve the efficiency of PV power generation: it could be possible either to develop low cost high efficiency solar conversion materials or to operate the PV system at maximum power point (MPP) for getting optimal output power. Because of the high cost of solar cells, it is necessary to operate the PV array at the maximum operating point. Therefore maximum power point tracking (MPPT) is considered as an essential part of PV generation system and is one of the key issues for researchers to reduce the effects of nonlinear characteristics of PV array [3].So far different MPPT algorithms have been proposed for optimization of PV output power, such as perturb & observe (P&O) [4–6], incremental conductance (INC) [7, 8], hill climbing [9, 10], neural network, fuzzy logic theory, and genetic algorithm [11–13]. However it has been observed that most of the MPPT methods are developed by assuming that solar irradiance is applied on the entire PV array uniformly. Unfortunately, the nonlinearity of solar irradiation is directly effecting the PV characteristic because of multiple local maxima (the mismatching problem) which can be exhibited on current-voltage (I
V curve) and power-voltage (P
V curve) of solar PV array if the entire array does not receive uniform solar irradiation.Although some researchers have worked on partially shaded condition (PSC) and fast changing solar irradiance MPPT [14–17], in [14], a two-stage MPPT with instant online V
o
c and I
s
c measurement was proposed. This MPPT is very simple to implement but an additional circuit is required to track the real maximum power point (RMPP) under nonuniform insolation conditions; a novel algorithm to track the global power peak (GPP) under partially shaded conditions based on several critical observations in conjunction with a DC-DC converter to accelerate the tracking speed with feed forward control is proposed in [15]. To ensure fast MPPT process with DC-DC converter duty cycle modulation under partial shading conditions and load variations with modified incremental conductance (INC) algorithm to track the GMPP is proposed in [16] and a modified incremental conductance algorithm under fast changing solar irradiance to reduce oscillation in solar module power at zero level and to mitigate the inaccurate response is discussed in [17].Among all the aforementioned MPPT algorithms, incremental conductance (INC) and perturb & observe (P&O) are commonly used for small and large scale PV power plants because both the algorithms operate in accordance with power against voltage (P
-
V) curve of PV module and tune the duty cycle of converter to ensure the next MPP point accordingly. In P&O steady state oscillation occurred because perturbation continuously changes in both the directions to maintain MPP under rapidly changing solar irradiance which causes system to be less efficient and to have more power losses [6, 18]. However, the conventional incremental conductance method determines the slope of PV curve by varying the converter duty cycle in fixed or variable step size until the MPP is achieved and in this way oscillation under rapidly changing solar irradiance is reduced with greater efficiency but due to complicated algorithm speed is slow.As discussed that nonlinear solar irradiance produces significant fluctuation in PV output voltage (V
P
V). So far, no considerable work is done to minimize the fluctuations of V
P
V terminal voltage of MPPT controller which is directly related to optimizing the efficiency and reducing the MPP tracking time. In this paper a direct control incremental conductance with simple moving voltage average (SMVA) technique is proposed. Using SMVA we examined the variability of V
P
V among different PV array configurations with nonuniform solar irradiance to aggregate the plant output at varying timescales. The simulation of proposed model is performed in MATLAB/Simulink and results are provided with comparison of conventional fixed step direct control incremental conductance method. The comparison results reveal that the proposed SMVA method provides better output by eliminating the steady state oscillations and greater output which is fast and accurate with response to variation of solar irradiation.In Section2 of this paper an overview about conventional and fixed step direct control INC is given and proposed SMVA technique is discussed in Section 3. Section 4 is about the case example and in Section 5 results are discussed, and finally in Section 6 conclusion is drawn.


## 2. Direct Control Incremental Conductance MPPT Method

Traditional conventional incremental conductance INC is based on two independent control loops as shown in Figure1(a). The first loop uses the incremental and instantaneous conductance to generate the error signal, and the second 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 nonuniform solar irradiance the slope of P
-
V characteristics curves (d
P
/
d
V
≠
0) at MPP.Figure 1
Block diagrams of INC MPPT algorithms implementation techniques; (a) reference voltage control; (b) direct duty ratio control.
(a)
(b)Therefore, a direct control incremental conductance method is proposed in [19–21] to simplify the control circuit, in which second loop, the proportional-integral (PI) controller, is eliminated as shown in Figure 1(b), in which duty cycle is adjusted into the algorithm and, to recompense the PI controller error detection function, a small marginal error of 0.002 is attuned in code. Now rewriting (1) of INC into direct control INC with fixed duty cycle and small marginal error, new equation comes out as (2):(1)
d
I
d
V
+
I
V
=
0
,
(2)
d
I
d
V
+
I
V
=
e
I
C
.So, now INC equations can be rewritten as(3)
d
I
d
V
+
I
V
=
e
I
C
≅
0
,
d
I
d
V
+
I
V
=
e
I
C
>
0
,
d
I
d
V
+
I
V
=
e
I
C
<
0
,where e
I
C is reported as an error in incremental and instantaneous conductance. The error (e
I
C) is set on constant basis or by following trial-and-error procedure [22]. But it has been observed that large marginal error provided faster convergence to MPP but produces unnecessary steady state oscillations, whereas small marginal error produces less steady state oscillation with slow convergence which tends to decrease 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 as ripple in solar PV generator voltageV
P
V under nonuniform solar irradiance. The proposed technique is inspired by advantages of practical simple moving average (SMA) model which is frequently used in financial markets to form a trend following indicator by reducing price fluctuations. Herein, SMVA does not predict price direction but rather defines the voltage direction with a lag because it is based on solar irradiation to compute and average the irradiation signal in time series analysis. The moving average is a simple low pass FIR (Finite Impulse Response) filter commonly used for smoothing an array of sampled data/signal; so far SMA is effectively used by different scholars [22, 23] in engineering characteristic reducing noise in random samples while retaining a sharp step response and computing the monitoring values to predict the future data.Although several other soft computing methods have been developed, as we can find in the works of Stevenson and Porter [24], Hansun and Subanar [25–27], and Popoola et al. [28, 29], moving average method is still considered as the best method by many researchers due to its easiness, objectiveness, reliability, and usefulness.Therefore, SMA technique is adopted for reducing the oscillatory effect ofV
P
V under nonuniform solar irradiation conditions. The proposed simple moving voltage average (SMVA) model is developed by following (4) in conjunction with fixed step direct control incremental conductance MPPT as shown in Figure 2, where X
(
n
) and Y
(
n
) are input and output signal of the SMVA, respectively, and (N) is the size of the moving average window, which holds the number of samples of the input signal as per defined limit and operates by averaging the number of points from the input signal to produce each point in the output signal [30]:(4)
∑
n
-
N
-
1
n
X
k
=
∑
n
-
N
n
-
1
X
k
-
X
n
-
N
+
X
n
,
Y
n
=
1
N
∑
n
-
N
-
1
n
X
k
.A certain size of SMVA moving block diagram is shown in Figures 3(a) and 3(b), where (N) is moving along with the array size compiled from the input signal, one element at a time, and the average of all elements in the current window is the output of the SMVA. When calculating successive values, a new value comes into the sum and an old value drops out by replacing each data point with the average of the neighboring data points defined within the span. The proposed SMVA model flow chart in conjunction with INC is depicted in Figure 4.Figure 2
Proposed simple moving voltage average (SMVA) with incremental conductance MPPT connection.Figure 3
(a) Moving average circuit. (b) Block diagram ofN-order simple moving average (SMA) circuit.
(a)
(b)Figure 4
Flow chart of proposed simple moving voltage average (SMVA) model with direct control incremental conductance.The proposed SMVA model is computed by following(5)
S
M
V
A
=
X
i
+
0
+
X
i
+
1
+
⋯
+
X
i
+
n
-
2
+
X
i
+
n
-
1
n
.In technical analysis, the number of sample points N is stochastic. It depends on nonuniformity of solar irradiance one is concentrating on. One characteristic of the SMVA is that if the data have an intermittent fluctuation, then applying SMVA of that period will eliminate that variation (with the average always containing one complete cycle). If 20 measurements, M
1 through M
20, are available, the successive 5-period simple moving averages, for example, are as follows:(6)
S
M
V
A
5
=
M
1
+
M
2
+
M
3
+
M
4
+
M
5
5
,
S
M
V
A
6
=
M
2
+
M
3
+
M
4
+
M
5
+
M
6
5
,
S
M
V
A
7
=
M
3
+
M
4
+
M
5
+
M
6
+
M
7
5
,
⋮
S
M
V
A
20
=
M
16
+
M
17
+
M
18
+
M
19
+
M
20
5
.Technically it is not possible to compute a 5-period moving average until 5 periods’ data are available. That is why the first moving average in the above example starts with SMVA5.In Figure5 an output signal of SMA is given where fluctuated (noisy) signal is smoothed by following (6), with 10 and 20 data points, where it can be observed that as the filter length increases (the parameter N) the smoothness of the output increases.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 moving average filters buffer size.


## 4. Case Example

Roof top centralized PV system installed at Zhejiang University, Yuquan Campus, College of Electrical Engineering Building, is taken as an example as shown in Figure6. In fact the installed PV system is regarded as a good one because of the same module and facing the sun in the same angle and direction. Therefore irradiation of these panels is supposed to be uniform. However, one should notice the chiller, water storage tank, and weather data collection unit cause shading effects on adjacent panels as in red circles it can be seen.Figure 6
Roof top PV system installed at ZJU.With reference to ZJU roof top PV system, a 3 KW system was designed by using a 37-watt PV module to quantify the analysis; PV panel specifications are shown in Table1. Approximation is made such that the PV panel peak power reduction rate is directly proportional to shading effects. Therefore, irradiance is estimated as (1) normal PV panel: 1000 W/m2 and (2) shaded PV panel between 768.36 W/m2 and 426.96 W/m2 as shown in Figures 7(a) and 7(b).Table 1
Electrical characteristic data of Solkar 36 W PV module.
Description
Rating
Maximum power (P
m
a
x)
37.08 Wp
Voltage at maximum power (V
m
p)
16.56 V
Current at maximum power (I
m
p)
2.25 A
Open circuit voltage (V
o
c)
21.24 V
Short circuit current (I
s
c)
2.55 A
Total number of cells in series (N
s)
36
Total number of cells in parallel (N
p)
1Figure 7
Centralized PV system. (a) Uniform solar irradiance. (b) Shaded system.
(a)
(b)According to Figures7(a) and 7(b), arrays A, B, and C with different irradiance I
V
-
P
V characteristic curves are drawn in Figure 8 in which multiple maximum power points due to irradiance mismatch are observed.Figure 8
(a)I
V characteristic curves, (b) P
V characteristic curves of PV array at 1000 W/m2 and mismatch irradiance levels.
(a)
(b)


## 5. Results and Discussions

To validate the performance of proposed simple moving voltage average (SMVA) technique under nonuniform solar irradiation, a MATLAB/Simulink model was developed as shown in Figure9, consisting of 3 KW PV array, a DC-DC boost converter (in Table 2 its component values are given), and a fixed step direct control incremental conductance MPPT controller with the SMVA technique.Table 2
Boost converter components values.
Component
Value
Unit
Capacitor (C)
93.75
uF
Inductor (L)
1.66
mH
Resistor (R)
53.3
Ohm
Rated input voltage
200
VDC
Rated output voltage
400
VDC
Rated output power
3
KW
Maximum average DC current
7.5
Amps
Switching frequency
16
KHzFigure 9
MATLAB/Simulink model of SMVA MPPT controller with DC-DC boost converter.At the first step of the simulation, a nonuniform solar irradiation is applied to the PV array where irradiation was set to 800 W/m2 at t
=
0.0 s and decreased to 600 W/m2 at 0.02 s and increased back to 1000 W/m2 at t
=
0.04 s; finally the irradiation decreased from 800 W/m2 to 600 W/m2 from 0.06 s to 0.1 s, with 25°C constant temperature. In traditional PV systems photovoltaic voltage V
P
V is directly given as an input to MPPT controller but in the proposed model V
P
V is given as an input to the SMVA module 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 model buffer sizes (number of sample points) of N
=
10 and N
=
30 with a change in duty cycle Δ
d
=
0.001 are applied; simulation results are presented in Figure 10.Figure 10
Simple moving voltage average filter. In (a)V
P
V, (b), and (c), this signal is filtered output V
P
V with SMVA, and (d), (e), and (f) are zoomed from (a), (b), and (c).Figure10(a) is an output voltage (V
P
V) of the PV array which is given as an input to the SMVA module to perform voltage smoothing and reduce the fluctuation using a span of data points following (6) with the buffer sizes N
=
10 and N
=
30. Figures 10(b) and 10(c) reveal the output comparison differences of fluctuated V
P
V and smoothed output of the proposed SMVA technique; Figures 10(d), 10(e), and 10(f) are zoomed from (a), (b), and (c) at t
=
0.05 to t
=
0.07 seconds where differences can be easily observed between (d), (e), and (f); results clearly indicate that the proposed method works effectively to reduce the fluctuation and improve the stability of voltage. It is observed in Figures 10(e) and 10(f) that a smaller buffer size produces higher fluctuation; as the buffer size increases, the fluctuation decreases.To demonstrate the effectiveness of the proposed SMVA model Figures11(a), 11(b), and 11(c) show the variation of the duty cycle of fixed step direct control INC with Δ
d
=
0.001, 0.005, and 0.01 and stability of the proposed SMVA model, where N
=
10 and 30. In Figure 11(a), fixed step direct control INC and the proposed SMVA duty cycles with different Δ
d and N are depicted, whereas Figure 11(b) is exemplifying the maximum point (MP) tracking time (T
a), the fixed step INC reached MP at T
a
=
0.008 seconds, and the proposed SMVA model gained the same MP at T
a
=
0.0051 and  T
a
=
0.0058 seconds, respectively. Furthermore, Figure 11(c) is giving an idea about the stability of duty cycle at different Δ
d between INC and the proposed SMVA. The results clearly illustrate that performance of the proposed SMVA model is much better compared to the conventional fixed step INC with all the three step sizes Δ
d
=
0.001, 0.005, and 0.01 during steady and dynamic state conditions and optimum duty cycle reached faster with less oscillation. The disadvantages of the fixed step INC with direct control are eliminated by the SMVA, in which the change in duty cycle Δ
d became stable because of extremely small d
P
/
d
V around MP, according to the change in the error absolute value between the instantaneous conductance and the incremental conductance.Figure 11
Duty cycle: fixed step INC controller withΔ
d
=
0.001, 0.005, and 0.01 and proposed method with N
=
10  and 30.
(a)
(b)
(c)Furthermore, to inspect the effectiveness of the proposed technique under nonuniform solar irradiation, different scenarios were simulated with a change in duty cycleΔ
d
=
0.001, 0.005, and 0.01 and the SMVA buffer size number was adjusted at N
=
10. Results are shown in Figures 12 and 13, where magenta color is representing the simple fixed step direct control INC’s output voltage and power and blue lines are for the proposed SMVA outputs. Results are showing that performance of the proposed technique is much better than that of fixed step direct control incremental conductance method at different duty cycle Δ
d step changes. It can be easily observed that the output voltage and power of the proposed technique give greater efficiency with more stability at all the different step size changes as compared to direct control INC, as it can be seen in Figures 12(a), 12(b), and 12(c) as Δ
d increases from 0.001 to 0.01, and INC’s output voltage decreases from the range of 385–407 volts to 374–397, where the upper limit decreases to 10 volts and the lower limit went down to 11 volts. In the SMVA output voltage remains higher than the INC’s within the range of 387–410 volts to 385–405 with the change in upper limit of 5 volts and lower limit to 2 volts. In the same way, in Figures 13(a), 13(b), and 13(c) output power comparisons between INC and the proposed SMVA method can be observed at Δ
d
=
0.001, and INC’s output power is between 2775 and 3100 watts. At the same duty cycle SMVA output power is 2825–3150 watts and at Δ
d
=
0.01 INC’s output power is 2625–2955, whereas SMVA output power is 2750–3055 watts.Figure 12
Output voltage comparison withΔ
d
=
0.001, 0.005, and 0.01 and N
=
10.
(a)
(b)
(c)Figure 13
Output power comparison withΔ
d
=
0.001, 0.005, and 0.01 and N
=
10.
(a)
(b)
(c)Figures12 and 13 show that the proposed simple moving voltage average (SMVA) technique with direct control incremental conductance MPPT method can efficiently deal with the tradeoff between dynamic response speed and steady state accuracy. The steady state oscillations are almost eliminated because of extremely small d
P
/
d
V around MPP, as shown in Figure 10(f), the ripple voltage is less than 1.0 volt. The dynamic performance is obviously better than that with fixed step direct control INC.Furthermore, Tables3(a) and 3(b) surmise the measurement output voltage and power of INC and the proposed SMVA method with different buffer sizes N
=
10, 30, and 50 and change in duty cycle Δ
d
=
0.001, 0.003, 0.005, and 0.01 in order to verify the repeatability of the results, where the same tests were carried out at three different irradiance levels. It can be seen that, at Δ
d
=
0.001, INC and SMVA perform extremely close in most cases because of small change in duty cycle, as it is reported in [31, 32] that smaller Δ
d reduces the steady state losses caused by the oscillation of the PV operating point around the MPP, but it makes the algorithm slower and less efficient in the case of rapid change in solar irradiation and larger step size contributes to faster dynamics but excessive steady state oscillations, resulting in a comparatively low efficiency as it can easily be seen in Figures 12 and 13 and Tables 3(a) and 3(b) as change in duty cycle increases from Δ
d
=
0.001 to 0.01, INC’s output voltage and power decrease, and fluctuation increases. From the above study, it is observed that in most cases SMVA gives better results with more stability as compared to traditional fixed step direct control INC with faster tracking system under extreme weather conditions along with reduction in sustained oscillations, which verify that the proposed method is suitable for standalone PV system under extreme weather conditions not only in terms of bus voltage stability but also in overall system efficiency.Table 3
(a) Output voltage comparisons between INC and SMVA at differentΔ
d and N. (b) Output power comparisons between INC and SMVA at different Δ
d and N.
(a)
Δ
d
0.001
0.003
0.005
0.01
INC
SMVA (N =)
INC
SMVA (N =)
INC
SMVA (N =)
INC
SMVA (N =)
Irr. (W/m2)
10
30
50
10
30
50
10
30
50
10
30
50
600
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
386.1
800
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
394.6
1000
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)
Δ
d
0.001
0.003
0.005
0.01
INC
SMVA (N =)
INC
SMVA (N =)
INC
SMVA (N =)
INC
SMVA (N =)
Irr. (W/m2)
10
30
50
10
30
50
10
30
50
10
30
50
600
2827
2861
2861
2861
2798
2861
2861
2861
2751
2795
2795
2795
2687
2795
2795
2795
800
2953
2986
2986
2986
2922
2988
2988
2988
2874
2919
2919
2919
2804
2919
2919
2919
1000
3081
3118
3118
3118
3039
3118
3118
3118
2992
3047
3047
3047
2931
3047
3047
3047


## 6. Conclusion

In this paper, simple moving voltage average (SMVA) technique with fixed step direct control incremental conductance method was employed. Simulation results show that proposed technique is able to reduceV
P
V oscillations, thereby reducing the power losses faced by the conventional INC algorithm under nonuniform solar irradiation. Also this method is able to improve not only the steady and dynamic state but also the design efficiency of system. In conclusion the proposed method performs accurately and better than the conventional INC algorithm and simulation results verify the feasibility and effectiveness of the proposed method.



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*Source: 479178-2015-12-21.xml*