An Improved MPPT Method for PV system with Fast ...

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2016.2599899, IEEE Transactions on Industry Applications IEEE TRANSACTION ON INDUSTRY APPLICATIONS

1

An Improved MPPT Method for PV system with Fast-Converging Speed and Zero Oscillation Xingshuo Li, Huiqing Wen, Member, IEEE, Lin Jiang, Member, IEEE, Weidong Xiao, Senior Member, IEEE, Yang Du, Member, IEEE, and Chenhao Zhao

Abstract—Maximum power point (MPPT) tracking is essential for Photovoltaic (PV) systems to ensure the highest power output of PV arrays under any environmental condition. Comparing to other techniques, the Beta method shows advantages in terms of tracking speed, steady state performance, and simple implementation. However, the conventional Beta can be further improved by minimizing oscillations around the maximum power point (MPP) under steady state and increasing tracking speed in response to rapid changing of irradiance or temperature. An improved Beta-parameter based MPPT method is proposed in this paper to achieve the above objectives. An adaptive scaling factor is introduced and utilized in the MPPT mechanism, which enhances the tracking speed and is easily applied for any PV power system. Furthermore, the proposed method can identify and maintain the middle point of the three-level perturbations, which eliminate the oscillations at steady state. The control mechanism is not limited by specific operating conditions and illustrates superior performance over traditional methods with regards to transient response and steady state performance, which contributes to effective solar power harvesting. Followed by theoretical analysis, the simulation and experimental evaluation validate the claimed advantages of the proposed MPPT solution. Index Terms—Maximum power point tracking (MPPT), photovoltaic (PV) system, fast-converging speed, zero oscillation.

I. I NTRODUCTION Photovoltaic (PV) energy is gaining popularity and regarded as one of the most important sustainable energy sources recently. Since the output power of PV modules shows strong nonlinear characteristics, which heavily depend on the environmental conditions such as irradiance and temperature, how to extract the maximum possible power from the installed PV systems under various environmental conditions is still a challenging problem. Nowadays there have been many Maximum Power Point Tracking (MPPT) methods proposed to address this problem, such as Perturb and observe (P&O) [1–3], HillClimbing (HC) [4], incremental conductance (INC) [5–7], Beta method [8, 9], Fuzzy-logic method [10–12], Parabolic prediction method [13, 14] and other advanced methods [15– 21]. TABLE I illustrates the classification of various MPPT methods according to their step-size features in steady-state and transient stages respectively. P&O, HC and INC belong to the first category. They are widely used in industry due to low cost and easy implementation. A fixed step size is used for both the transient and the steady-state stages, thus, it’s difficult to optimize their steady-state and the dynamics performance simultaneously. They are easily confused for the transient operations, which results in the drift of the operating

TABLE I C LASSIFICATION OF MPPT

METHODS IN TERMS OF THE STEP SIZE FEATURES

No.

Transient Stage

Steady-state Stage

Methods

1

Fixed

Fixed

P&O [1–3], HC [4] and INC [5–7]

2

Variable

Variable

MAHC [27], VSSINC [23], INR [26], Delta P&O [24], PI-P&O [28], etc

3

Variable

Fixed

Beta [8], ZA-P&O [33] and Modified INC [15]

point from the maximum power point (MPP) [7]. Besides, they exhibits fluctuation around the MPP during the steady-state operation [22], which adds the power losses. The second category MPPT methods utilize a variable step size for both of the transient and the steady-state stages [23– 32], such as modified adaptive hill climbing (MAHC) [27], variable step size incremental conductance (VSSINC) [23], incremental resistance (INR) [26], Delta P&O [24], and PI-P&O [28] etc. The step sizes for these methods are automatically adjusted according to the gradient of the P-V curve [23–25], P-I curve [26] or P-D curve [27]. Therefore, a smaller steadystate oscillations and faster dynamic behavior are achieved compared with the first category methods. However, key parameters such as the scaling factor must be used and tuned to balance the dynamic and steady-stage performances [23]. A large scaling factor increases the convergence speed during the transient stage, however, it will increase oscillations around the MPP for the steady state. Contrarily, when the operating point is close to the peak of P-V curve, P-I curve or P-D curve, a small scaling factor is adopted, which can minimize the steady-state oscillations, however, the convergence speed of the system towards the MPP becomes slow. Fig. 1 illustrates the comparison of MPPT methods for transient and steady-stage operations. Both P&O and VSSINC methods exhibit significant oscillations in steady state, furthermore, the tracking-speed of P&O for transient is extremely slow. Although the dynamic performance with VSSINC is improved, it shows wrong step change in duty cycle for sudden irradiance variation. The third category MPPT methods adopt a variable and a fixed step size for the transient and the steady-state stages respectively, such as the Beta method proposed by Jain and Agarwal [8], zero-oscillation adaptive-step P&O (ZA-P&O)

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2016.2599899, IEEE Transactions on Industry Applications

Duty Cycle(%)

Voltage(V)

IEEE TRANSACTION ON INDUSTRY APPLICATIONS

2

No ocillations

fast tracking speed

correct step change

Time(s)

(a)

Duty Cycle(%)

Voltage(V)

P&O VSSINC

with the changes of parameter β due to the environmental changes. Therefore, the proposed method can achieve a faster tracking convergence speed compared to the conventional Beta method. The ZOPO method identifies the middle point of the three-level perturbations under the steady-state operation. Thus, the steady-state oscillations can be totally eliminated, which can further improve the tracking efficiency. By comparison with the P&O method and the VSSINC method, main advantages of the proposed method are illustrated in Fig. 1, which can be summarized as follows: (1) high steady-state tracking efficiency by totally eliminating oscillations; (2) the dynamic efficiency is improved by employing an adaptive scaling factor; (3) the wrong step change caused by the rapid irradiance change is eliminated.

steady−state ocillations

II. R EVIEW OF THE CONVENTIONAL B ETA METHOD

slow tracking speed wrong step change

Time(s)

(b) Fig. 1. Performance comparison of MPPT methods: (a) the proposed MPPT method; (b) P&O and VSSINC method.

[33] and modified incremental conductance with MPP locus prediction (Modified INC) [15]. [9, 34] comprehensively evaluated main MPPT methods in terms of the available power, PV voltage ripple, and dynamic response through simulation and experiments. The results show that the Beta method exhibits a fast tracking speed in the transient, small oscillations in the steady state and easy implementation since it tracks an intermediate variable β rather than the change of the power. However, the potential of the conventional Beta method is not fully exploited in two perspectives, namely, the oscillations around the MPP under steady-state operations and a limited converging speed for rapidly changing environmental conditions due to a fixed scaling factor. [35] optimized the performance of this method by identifying the range of the parameter β for various environmental conditions, furthermore, a optimal scaling factor was selected through parameter sweeping. However, the optimal scaling factor resulting from this process is just suitable for limited operating conditions, furthermore, the oscillations still occur in the steady-state stage. Originated from [35], an improved MPPT method is proposed in this paper. The proposed method consists of two stages: 1) the Adaptive Scaling Factor Beta (ASF-Beta) for the transients; and 2) the Zero Oscillations Perturb and Observe (ZOPO) for the steady state. The ASF-Beta method implements an adaptive scaling factor instead of the fixed scaling factor in the conventional Beta method. The process to determine the optimal scaling factor is eliminated and the guiding parameter βg is removed in the practical implementation. Thus, the ASF-Beta becomes less dependent on the PV system. Besides, the step size is automatically updated

The conventional Beta method was firstly proposed by Jain and Agarwal in [8]. The basic principle of this method is to track an intermediate variable β rather than the change of the power, which is expressed as: (i ) pv − c × vpv (1) β = ln vpv where vpv and ipv are the PV module output voltage and output current respectively. c = q/(Ns AKT ) is the diode constant, where q is the electron charge 1.602 × 10−19 C, A is the diode ideality factor, K is Boltzmann constant 1.38 × 10−23 J/K, T (in Kelvin) is the temperature of the p–n junction, and Ns is cell number of the PV module. This method has two stages: the transient stage and the steady-state stage, which adopt the variable step and fixed step respectively. The flowchart of this method is shown in Fig. 2. Firstly, the voltage and current are measured, then the actual values of βa are continuously calculated. If the βa is within the bounding range of (βmin , βmax ), the Beta method turns into steady-state stage, otherwise the Beta method switches into the transient stage and the P&O method will be implemented. In the transient stage, a guiding parameter βg is adopted in calculating the variable step size ∆D, which can be expressed as: ∆D = N × (βa − βg ) (2) where N is the scaling factor. ^ƚĂƌƚ ^ĞŶƐĞs;ŬͿ͕/;ŬͿ ĂůĐƵůĂƚĞɴĂсůŶ;/;ŬͿͬs;ŬͿͿ̢ ̢ĐΎs;ŬͿ ^ƚĞĂĚǇͲƐƚĂƚĞ ^ƚĂŐĞ

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Fig. 2 indicates that the range of the parameter β, (βmin , βmax ) and parameter βg , needs to be identified. According



3

TABLE II Current(A)

4

UNDER VARIOUS IRRADIANCE AND TEMPERATURE CONDITIONS

No.

Irradiance

temperature

β

1 2 3 4

1000W/m2

45◦ C

-15.4505 -18.3431 -15.9587 -19.0214

5◦ C

1000W/m2

45◦ C 5◦ C

300W/m2 300W/m2

2

−10 −20

No.1 No.2 No.3 No.4 β1 β2 β3 β4

MPP MPP

Power(W) & β

40

0

βmax = β1

β1=−15.4505

−20

β3=−15.9587

βmin = β4

−40 0

MPP

MPP

20

5

10

15 Voltage(V)

B

0 0

80

β2=−18.3431

β4=−19.0214

20

2

1000W/m 400W/m2 D

C load line 2

−30 0

60

A load line 1

5

10

15

20

B

βmax = −15.45

A

25

∆D = N* (βD − βg)

β

VALUES OF β

25

Fig. 3. Range of β and power under various irradiance and temperature conditions.

to [8, 34, 35], the range of the parameter β depends on the environmental conditions of the PV module, such as the irradiance and temperature. TABLE II illustrates the environmental conditions and the calculated magnitudes of β. The range of the parameter β is determined as βmin = −19.02 and βmax = −15.45. Fig. 3 shows that the the range of β is narrow for wide environmental conditions. In [35], the middle value between βmin and βmax is used for βg , namely βg = −17.24. Fig. 4 illustrates the I-V curve and β-V curves under a sudden irradiance changes between 1000W/m2 and 400W/m2 . The solid lines represent the I-V curves, two dash lines are the load lines: load line 1 and the load line 2. The intersection point between the load line 1 and the I-V curve under 1000W/m2 is the point A, which represents the MPP under 1000W/m2 . Similarly, the point C represents the MPP under 400W/m2 , which is the intersection point between the load line 2 and the I-V curve under 400W/m2 . When the irradiance is suddenly decreased from 1000W/m2 to 400W/m2 , since the duty cycle of the dc-dc converter at the beginning remains unchanged, thus, the operating point is still located at the load line 1 and the operating point switches immediately from A to B, which is the intersection point between the load line 1 and the I-V curve under 400W/m2 . In the β-V curve, the point A lies within the defined range, so a fixed step is implemented and the operating point fluctuates around A. When the irradiance is decreased to 400W/m2 , the operating point immediately switches from A to B, which is out of the bounding range. Then a variable step is implemented, the operating point keeps moving towards C, which is the MPP under 400W/m2 . Similarly, when the irradiance is suddenly increased from 400W/m2 to 1000W/m2 , the operating point firstly switches from C to D, then from D to A. With the conventional Beta method, the converging speed for rapidly changing environmental conditions depends on

βmim = −19.02

∆D = N * (βB − βg)

5

10

15 Voltage(V)

βg = −17.24

C

20

25

Fig. 4. I-V curve and β-V curves under the sudden irradiance changes between 1000W/m2 and 400W/m2 .

the scaling factor. In [35], the performance of this method was optimized by identifying the range of the parameter β for various environmental conditions, furthermore, the scaling factor was optimized through parameter sweeping. However, the optimal scaling factor resulting from this process is just suitable for limited operating conditions, furthermore, the oscillations are still observed in the steady-state stage. Thus, the potential of the Beta method needs further optimization for both steady-state and dynamic operations. III. P ROPOSED MPPT M ETHOD The proposed MPPT method consists of two stages: 1) the Adaptive Scaling Factor Beta (ASF-Beta) for transient, as shown branches (A) to (D) in Fig. 5; and 2) the Zero Oscillations Perturb and Observe (ZOPO) for the steady state, as shown branches (E) to (H) in Fig. 5. A. Adaptive Scaling Factor Beta method (ASF-Beta) Compared to (2), the ASF-Beta removes the guiding parameter βg and the step size is updated as: { N × (βa (k) − βmin ), for βa (k) > βmax (3a) ∆D = N × (βa (k) − βmax ), for βa (k) < βmin (3b) where (3a) and (3b) represent the expressions for the variable step size when the irradiance is decreased and increased respectively, βa (k) is the present value of β. The adaptive scaling factor N shown in (3) is derived by { 1, for βa (k − 1) < βmax (4a) N= βa (k)−βmin for βa (k − 1) > βmax (4b) βa (k−1)−βa (k) , { 1, for βa (k − 1) > βmin (5a) N= βa (k)−βmax for βa (k − 1) < βmin (5b) βa (k−1)−βa (k) , where (4) and (5) represent the expressions for the adaptive scaling factor N when the irradiance is decreased and increased respectively, βa (k − 1) is the previous value of β. When the irradiance is decreased from 1000W/m2 to 400W/m2 , as discussed above, the operating point immediately switches from A to B, as show in Fig. 6(a). Since the present value of β, namely βB , is larger than βmax , the step size should be updated by (3a). Furthermore, the previous value, βA , is smaller than βmax . Therefore, the scaling factor N is set



4

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Fig. 5. Flowchart of the proposed MPPT method. A

2

B

B1

B2 (B)

(A)

0 0

5

−10 β

%

1=

% β

15

20

25

B1

% ( %%

=

β % − β PLQ β % − β %

%

B2

= −15.45

A

$

β

max

β %

C (B)

10 B

1000W/m2 400W/m2

load line 1

β

Current(A)

4

−20 β

mim

C

= −19.02

&

E

β

(

PLQ

−30 0

5

10

15 Voltage(V)

20

25

(a)

9ROWDJH9

(b)

Fig. 6. Principle of the ASF-Beta method: (a) tracking process for irradiance decreasing from 1000W/m2 to 400W/m2 ; (b)derivation of the adaptive scaling factor N .

to 1 according to (4a), and the ASF-Beta is implemented with the branch (A), as shown in Fig. 5. Then the operating point moves from B to B1, where the present and previous values are updated as βB1 and βB respectively. Since both calculated βB1 and βB are larger than βmax , the scaling factor N is derived by (4b) and the branch (B) is implemented. Fig. 6(b) illustrates the process to derive the scaling factor N . Here, |BB1 | and |B1 E| are used to calculate the distance between B and B1, B1 and E respectively. The scaling factor N is defined as the ratio between |BB1 | and |B1 E|, which can be expressed by N=

|B1 E| |βB1 − βmin | = |BB1 | |βB − βB1 |

(6)

If B1 is closer to B rather than E, the ratio between |BB1 | and |B1 E|, namely N , becomes large, which results in large step size, and vise versa. As shown in Fig. 6, the operating point moves from B1 to B2. The ASF-Beta will be implemented through branch (B) since the calculated both βB2 and βB1 are larger than βmax . After repeating this process for several times, the transient process is finished since the calculated parameters β for the

present and previous points locate within the bounding range, then the ZOPO will be implemented for the steady state. When the irradiance is increased or the load is changed, similar processes to derive the parameter N can be analyzed, which will not present here due to the length constraint of the paper. B. Zero Oscillations Perturbation and Observe method (ZOPO) According to [1], using the conventional P&O method, the duty cycle for the steady state oscillates with three different levels, which can guarantee periodic and stable oscillations around the MPP point, as shown in Fig. 7(a), where Tp is the sampling period. Fig. 7(a) shows that a common middle level, Dmid , occurs twice in every period of 4Tp . Furthermore, the corresponding power level, Pmid , is higher than the neighboring other two levels. Since no way of identifying a environmental change is adopted in conventional MPPT methods, the perturbations of the operating points are continuously repeated even though the MPP has been tracked, as shown in Fig. 7(a).



mid

Pmid

Dmid

Dmid

Pmid

P

mid

Dmid

4Tp

Dmid

4Tp

P

P

mid

Power(W)

P

Duty Cycle(%)

Duty Cycle(%)

Power(W)

Tp

5

Pmid

mid

Dmid = D1 = D3 D1

D4

D3 D2 4Tp

Time(s)

Time(s)

(a)

(b)

Fig. 7. Typical power and duty cycle waveforms for the steady-state operation with two MPPT method: (a)the conventional P&O method; and (b)the ZOPO method.

Power(W)

1000W/m2 B

A

counter = 0 counter ++

counter = 0

950W/m2

counter ≥4

Duty Cycle(%)

C

Dmid

Zero Oscillation

D3 D2

D4

D1 (E)

(F)

(G)

whole period of 4Tp , the proposed method will finally identify the middle level at the point B as the steady-state output power since the counter reaches four. Thus, the branch (G) is implemented and no oscillation occurs. When the irradiance is decreased to 950W/m2 , the proposed method will calculate the power at the point C. Once ∆P is detected larger than e, the branch (H) is implemented and the counter is reset as zero.

(H)

Time(s)

TABLE III M AIN P RODUCT PARAMETERS OF THE MSX-60W

Fig. 8. Tracking process of the ZOPO method for the steady-state operation.

To address this issue, the ZOPO is used to identify and maintain the middle point of the three-level perturbations, which eliminates the oscillations for the steady state. Fig. 7(b) illustrates the principle of this idea, where D1, D2, D3 and D4 are the values of the duty cycle in every period of 4Tp . The first step of ZOPO is to identify the middle point of the three-level perturbations and the criterion is defined as: “D1 equals to D3” or “D2 equals to D4”. Once the defined criterion is met, the middle point Dmid will be identified. Then a counter is activated automatically. Considering the effects of the noise and measurement errors, “four” is defined as the threshold for the counter. Namely, once the counter reaches four, the ZOPO will consequently maintain at the highest middle power level until another environmental variation is detected. The power difference ∆P during each period is calculated and a threshold e is used to determine weather an actual environmental variation has been detected considering the effects of the noise and measurement errors. If ∆P is larger than e, it means that the environmental condition has been changed. Fig. 8 illustrates the tracking process of the ZOPO for the steady state. The initial irradiance is 1000W/m2 , the calculated duty cycle values will not meet the defined criterion of the ZOPO. Thus, the counter is zero. According to the Fig. 5, the proposed method goes through the branch (E) for the steady state. The counter remains as zero until it reaches the point A, where the Dmid is detected for the first time since D2 equals to D4, as shown in Fig. 8. Then the branch (F) is implemented and the counter is automatically added. After the

Parameter

Symbol

Value

Maximum power Voltage at maximum power Current at maximum power Open-circuit voltage Short-circuit current Temperature coefficient of Voc Temperature coefficient of Isc

Pmpp Vmpp Impp Voc Isc Kv Ki

60W 17.1V 3.5A 21.1V 3.8A −80mV /◦ C 0.065%/◦ C

/ &LQ

39PRGXOH

3:0 *HQHUDWRU

LSY 0337

&RXW

YSY

%RRVWFLUFXLW

5ORDG

/RDG

0337 &RQWUROOHU

Fig. 9. PV system with MPPT control

IV. S IMULATIONS Fig.9 shows a complete PV system model with the proposed MPPT algorithm. It includes a PV module, boost converter, resistive load and MPPT controller. The Solarex MSX-60W is used with its electrical parameters shown in TABLE III. Main specifications for the boost converter include: Cin (PV side) = 470uF , Cout (Boost circuit) = 47uF , L = 1mH, switching frequency (IGBT) = 10kHz. A variable resistor is used as



6

P&O VSSINC Beta Proposed

2

0.5

1

1.5

2

2.5

3

3.5

4

4.5 Duty Cycle(%)

Voltage(V)

0 0

Power(W)

Current(A)

4

20 10 0 0

0.5

1

1.5

2 2.5 Time(s)

3

3.5

4

4.5


60 40 20 0 0 70

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.5

1

1.5

2 2.5 Time(s)

3

3.5

4

4.5

60 50 40 30 0

(a)

(b)

Fig. 10. Simulation results of the P&O, VSSINC, Beta and the proposed method for the irradiance variation under strong intensity: (a) current and voltage; (b) power and duty cycle.

40

B2

B1

20

C

B

0 0.4 70 60

Current(A)

A

0.5

0.6

0.7

0.8

0.9

2 0

1

A

B1

B

6

−10

8

10

B

(E)

18

20 β

22

max

A

= −15.45

0.5

0.6

0.7 Time(s)

0.8

0.9

−30

1

6

8

10

Current(A)

D2 D1

A

D3

C D

20 0 2.4 70

2.5

2.6

60

2.7

2.8

14 16 Voltage(V)

18

20

D3 D2

2

(D)

D

17

18

19

20

2.5

2.6

2.7 Time(s)

2.8

2.9

(c)

−25 16

21

β

−15 −20

D1

load line 2 C

A

max

D3 D2

C

D1

D

(C)

(G)

22

1000W/m2 400W/m2

A

0 16 −10

2.9

(G)

(F)

(E)

50

12

(b) 4

60

βmim = −19.02

(G)

(F)

β

Power(W) Duty Cycle(%)

16

C

(a)

30 2.4

14

B2

(B)

30 0.4

40

12

C

B1

−20

(A)

40

40

B2

(G)

50

1000W/m2 400W/m2

load line 1

β

Duty Cycle(%)

Power(W)

4 60

17

18

19 Voltage(V)

20

= −15.45

βmim = −19.02

21

(d)

Fig. 11. Simulation results by using the proposed method: (a) power and duty cycle when the irradiance is decreased; (b)current, β, and tracking process when the irradiance is decreased; (c) power and duty cycle when the irradiance is increased; (d)current, β, and tracking process when the irradiance is increased.

the load. The sampling time for the MPPT controller, Tp , is calculated by 1 Tp ≥ Tε ∼ · ln(ε) (7) =− ξ · ωn √ √ where ωn = 1/ L · Cin , ξ = 1/(2 · Rmpp ) · L/Cin , and ε = 0.1 [1]. In this paper, Tp is set as 0.03s according to (7). A simulation comparison of the proposed MPPT method with other methods, such as P&O method [1], variable-stepsize INC (VSSINC) [23] and conventional Beta method [35], are carried out under different scenarios: irradiance variation under strong intensity, irradiance variation under weak intensity, and load variation. A. Irradiance Variation under Strong Intensity Fig.10 shows the simulation result for this scenario, where the irradiance level is decreased from 1000W/m2 to 400W/m2 at t = 0.5s and increased to 1000W/m2 at

t = 2.5s. During this period, the load resistance is fixed at 30Ω. Fig.10 shows that P&O takes the longest time to track the MPP due to a fixed step size. A total time of 1.35s and 1.38s are required to track the MPP when the irradiance is decreased and increased respectively. For the steady-state stage, three-level oscillations can be observed in Fig.10, which results in extra power losses. VSSINC and the conventional Beta method take less time than P&O but more time than the proposed method. When the irradiance is decreased to 400W/m2 , VSSINC exhibits longer time (0.93s and 31Tp ) to reach the MPP compared to the Beta method (0.42s and 14Tp ). In contrast, when the irradiance is increased to 1000W/m2 , VSSINC needs shorter time (0.51s and 17Tp ) to locate the MPP than the Beta method (0.63s and 21Tp ). During the steady-state stage, the VSSINC method exhibits smaller oscillations compared to that of the P&O method and the Beta method, thus it results in less power losses.



7

1

2

3

4

5

6

7

20 10 0 0

30 Power(W)

1 0 0

Voltage(V)


Duty Cycle(%)

Current(A)

2

1

2

3

Time(s)

4

5

6

7


20 10 0 0 80

1

2

3

1

2

3

4

5

6

7

4

5

6

7

60 40 20 0

(a)

Time(s)

(b)

Fig. 12. Simulation results of the P&O, VSSINC, Beta and the proposed method for the irradiance variation under weak intensity: (a) current and voltage; (b) power and duty cycle.

0.5

1

1.5

2

2.5

3

3.5

20 10 0 0

40 Power(W)

1 0 0

Voltage(V)


2

Duty Cycle(%)

Current(A)

3

0.5

1

1.5 2 Time(s)

2.5

3

3.5


30 20 0 70

0.5

1

1.5

2

2.5

3

3.5

0.5

1

1.5 2 Time(s)

2.5

3

3.5

60 50 40 0

(a)

(b)

Fig. 13. Simulation results of the P&O, VSSINC, Beta and the proposed method for the load variation condition: (a)current and voltage; (b) power and duty cycle.

Fig.10 indicates that the proposed method takes the shortest time among these other methods. Detailed tracking process is illustrated in Fig.11. Fig.11(a) and (c) show the enlarged waveforms of power and duty cycle with the proposed method when the irradiance is changed, and Fig.11(b) and (d) show the movement of the corresponding operating points on the I– V curve, β–V curve. From t = 0s to t = 0.5s, the irradiance level is 1000W/m2 . The PV module operates at point A, as shown in Fig.11(b), and the branch (G) is implemented according to Fig. 5. At t = 0.5s, the irradiance is decreased from 1000W/m2 to 400W/m2 , thus, the operating point immediately switches from A to B along the load line 1. At the next sample point t = 0.52s, the point B is found, so the ASF-Beta is implemented through the branch (A), and then the operating point moves to the point B1. Since both of the points B and B1 are beyond the bounding range, the branch (B) is implemented and the operating point moves to the point B2. Since the point B2 is within the defined bounding range, the ZOPO is implemented with the branch (E). After a time of 6Tp , the condition “D1 = D3” or “D2 = D4” is met firstly at t = 0.76s, the ZOPO identifies the middle level of the three-level perturbations, so the branch (F) is implemented in the ZOPO. After a time of 4Tp , the middle level is finally detected, so the branch (G) is implemented. The duty cycle of the converter, and the power of the PV module is maintained at 38.3% and 23.555W respectively. No oscillations can be found. The PV module operates steadily at point C of the load line 2. When the irradiance is increased to 1000W/m2

at t = 2.5s, similar process is illustrated in Fig.11(c) and (d). B. Irradiance Variation under Weak Intensity Fig.12 shows the simulation results for this scenario: the irradiance level is decreased from 400W/m2 to 100W/m2 at t = 1s and increased to 400W/m2 at t = 4s. During the irradiance variation, the load resistance is fixed at 80Ω. Fig.12 shows that the proposed method presents the shortest time to locate the MPP, which are 0.42s and 0.36s for the irradiance falling and rising transients respectively. P&O takes the longest time, which are 2.16s and 2.22s respectively. Furthermore, VSSINC is unable to track the MPP for the irradiance falling transient within the whole steady-state period of 100W/m2 . The tracking speed of the conventional Beta method is slower than that of the proposed one especially for the irradiance rising transient. Simulation results under these two scenarios show that VSSINC exhibits wrong step change in duty cycle for sudden irradiance changing transients, as shown the duty cycle waveforms in Fig.10(b) and Fig.12(b). C. Load Variation Fig.13 shows the simulation results for this scenario: the load resistance is decreased from 60Ω to 30Ω at t = 0.5s, and then increased back to 60Ω at t = 2s. During this period, the irradiance level is kept constant at 600W/m2 . In term of the tracking speed, the results for the load variation scenario are similar to those obtained in the previous



8

3


Tracking Time(s)

2.5

dSPACE

2 1.5

PV emulator

Electronic load 1 0.5

Boost

0

2

1000W/m − 2 400W/m

2

400W/m − 2 1000W/m

2

400W/m − 2 100W/m

2

100W/m − 2 400W/m

60Ω− 30Ω

30Ω− 60Ω

Fig. 15. Experimental prototype of the PV system with MPPT control.

(a)

Power Loss(%)

40

TABLE IV M AIN COMPONENTS FOR THE PROTOTYPE


30 20 10 0

1000W/m2− 400W/m2

400W/m2− 1000W/m2

400W/m2− 100W/m2

100W/m2− 400W/m2

60Ω− 30Ω

30Ω− 60Ω

(b) 0.1


Power loss(%)

0.08

Parameter

Value

Electrolytic capacitor Cin (PV side) Electrolytic capacitor Cout (Load side) Inductor L IGBT Diode Current transducer Voltage transducer Switching frequency

470uF 47uF 1mH IRG4PH50U RHRG30120 LA25-NP LV25-P 10kHz

Ploss is defined as

0.06

Ploss =

0.04 0.02 0

400W/m^2

600W/m^2

1000W/m^2

(c) Fig. 14. Simulation results comparison of the proposed method with other methods: (a)tracking time; (b)tracking power loss; (c)steady-state power loss.

two scenarios. The proposed method is the fastest method to locate the MPP while the P&O method is the slowest one, as shown in Fig.13.

D. Evaluation Fig.14(a) illustrates the comparison results of the proposed MPPT method with other MPPT methods in term of the tracking time. Different cases are analyzed: the irradiance variation under strong intensity (falling and risng transients), the irradiance variation under weak intensity (falling and risng transients), and the load variation conditions (falling and risng transients), as shown in Fig.14(a) and (b). The comparison results show that the proposed method is the fastest method among these methods to locate the MPP while the P&O method is the slowest one in all cases. The VSSINC method is faster than the conventional Beta method when the irradiance or resistance is increased. Contrarily, the conventional Beta method is faster than the VSSINC method when the irradiance or resistance is decreased. Fig.14(b) illustrates the power loss comparison of the these MPPT methods for various scenarios. Here, the power loss

∑

∑ Pmax (t) − Ppv (t) ∑ Pmax (t)

(8)

where Pmax is the maximum possible power under a certain irradiance level, Ppv refers to the power extracted by the different methods, and t refers to the total tracking time required by the different methods to reach the MPP. Since the power loss during the transient stages determined mainly by the tracking speed, the calculated power loss with the proposed method is less than the other methods for most cases except for the scenario with the load resistance increased from 30Ω to 60Ω, as shown in Fig.14(b). Fig.14(c) represents the steady-state power loss comparison with these MPPT methods under the different irradiance levels. Due to a fixed step size, the power loss for the P&O method and the conventional Beta method are almost same, which are higher than other methods. The power loss for the VSSINC method is reduced compared with P&O method and the conventional Beta method. Since the proposed method eliminates totally the oscillations, the power loss of this method is the smallest one under all irradiance levels. V. E XPERIMENTAL R ESULTS In order to verify the effectiveness of the proposed method, an experimental prototype of the PV system with MPPT control was built up, as shown in Fig.15. The prototype incudes main components such as a boost converter, a PV emulator, a electronic load and a dSPACE controller. The specifications for the main components of the prototype are shown in TABLE IV. The PV emulator Chroma ATE-62050H-600S used was a programmable DC supply to emulate solar module characteristics. The dSPACE DS1104 was adopted as a control platform and various MPPT methods were implemented. The electronic



9

Ppv = 60W/div

Ppv = 60W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

5s/div

Ipv = 2.5A/div

(a)

(b)

Ppv = 60W/div

Ppv = 60W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

5s/div

5s/div

Ipv = 2.5A/div

(c)

5s/div

(d)

Fig. 16. Experimental results for the irradiance variation under strong intensity: (a)P&O; (b)VSSINC; (c)conventional Beta method; (d)the proposed method.

Ppv = 60W/div

Ppv = 60W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

10s/div

Ipv = 2.5A/div

(a)

(b)

Ppv = 60W/div

Ppv = 60W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

10s/div

(c)

10s/div

Ipv = 2.5A/div

10s/div

(d)

Fig. 17. Experimental results for the irradiance variation under weak intensity: (a)P&O; (b)VSSINC; (c)conventional Beta method; (d)the proposed method.



10

Ppv = 20W/div

Ppv = 20W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

5s/div

Ipv = 2.5A/div

(a)

(b)

Ppv = 20W/div

Ppv = 20W/div

Vpv = 5V/div

Vpv = 5V/div

Ipv = 2.5A/div

5s/div

5s/div

(c)

Ipv = 2.5A/div

5s/div

(d)

Fig. 18. Experimental results for the load variation condition: (a)P&O; (b)VSSINC; (c) conventional Beta method; (d) the proposed method.

load, IT8514C+, was used for load variation analysis. Since the PV emulator has a limited dynamic speed, which is much slower than that of a practical crystalline PV module [36]. Therefore, the sampling time Tp for the MPPT controller in the experiments is set as 0.3s. Fig.16 shows the experimental waveforms of the power, current and voltage of the PV emulator for the irradiance variation under strong intensity. The irradiance variation parameters in the experiments were set the same as those in the simulation. Specifically, the irradiance were set to change between 1000W/m2 and 400W/m2 . During the irradiance variation, the electronic load was fixed at 30Ω. Fig.16 shows that the proposed method exhibits the shorter time to track the MPP compared with the other methods. The tracking power loss is lowest among these methods. During the steady-state stage, no oscillations are observed by using the proposed method while the voltage oscillations with the other methods can be observed easily. Therefore, both of the steady-state and dynamic tracking power losses of the proposed method are lowest among these methods. Fig.17 represents the experimental result for the irradiance variation under weak intensity. Similar with the results obtained in the simulation, the proposed method shows the shortest tracking time, the lowest tracking power loss and the lowest steady-state power loss among these MPPT methods. As shown in Fig.17(b), the VSSINC method is unable to track the MPP during the 40s low-irradiance period, which results in highest tracking power losses. The steady-state

oscillations in voltage are oblivious for the P&O method and the conventional Beta method, especially for the 100W/m2 irradiance condition. Fig.18 illustrates the power, voltage and current waveforms of the PV emulator when the load toggles between 60Ω and 30Ω. The proposed method responses more rapidly than the other methods. Furthermore, it does not oscillate during the steady-state stage. The experimental comparison of the proposed MPPT method with the other MPPT methods is shown in Fig.19. The overall tracking time of the proposed method is 2.26s, which is 6 times, 4 times and 2 times shorter than that of the P&O method, the VSSINC method and the conventional Beta methods. Around 3.95% overall tracking power loss with the proposed method is observed, compared to 20.83%, 14.26% and 6.53% reduction than that of the P&O method, the VSSINC method and the conventional Beta method. The steady-state power loss of the proposed method is 3 times lower than that of the P&O method and the conventional Beta method, and 2 times lower than that of the VSSINC method. According to EN 50530, the static and dynamic MPPT efficiency measurements are performed with various MPPT methods. The static efficiency for the European Efficiency (ηEU R ) is given as [37]: ηEU R = 0.03 · η5% + 0.06 · η10% + 0.13 · η20% +0.1 · η30% + 0.48 · η50% + 0.2 · η100%

(9)

where the indices of 5%, 10%, etc., refer to power level of



11

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40

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30

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1000W/m − 2 400W/m

2

400W/m − 2 1000W/m

2

400W/m − 2 100W/m

2

100W/m − 2 400W/m

60Ω− 30Ω

W W W W

30Ω− 60Ω

7LPH

(a) (a)

Tracking loss(%)

40


30

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400W/m2− 1000W/m2

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100W/m2− 400W/m2

60Ω− 30Ω

WLQL

30Ω− 60Ω

W W W W

(b) 0.5

(b)


0.4 Power loss(%)

7LPH

Fig. 20. Dynamic test sequences according to EN 50530: (a)the test sequence for fluctuations between low and medium irradiance level; (b)the test sequence for fluctuations between medium and high irradiance level.

0.3 0.2

these methods. TABLE V shows the specific parameters for the two sequences.

0.1 0

400W/m^2

600W/m^2

1000W/m^2

TABLE V PARAMETERS OF THE TWO DYNAMIC TEST SEQUENCES FOR EN 50530

(c) Fig. 19. Comparison of the experimental results by using the proposed MPPT method and the other MPPT methods: (a)tracking time; (b)tracking power loss; (c)steady-state power loss.

corresponding fractions of standard test condition (STC)[37]. Then, the corresponding static efficiency can be calculated by ηstat,k =

Σk PP V · ∆T Pmax · TM

(10)

where k refers to the power level component, e.g., 5% component, and PP V is the sampled value of the power from the PV emulator, ∆T is the sampling period, Pmax is the theoretical maximum value of the power, and TM is the total measurement time. The dynamic efficiency is determined by two test sequences with different irradiance levels. Specifically, sequence A is changing from 100W/m2 and 500W/m2 , and sequence B is changing from 300W/m2 and 1000W/m2 , as shown in Fig.20 [38]. The time t1 , t2 , t3 and t4 determine the speed of irradiance change, and n is the number of repetitions of the pattern. Then, the dynamic efficiency can be calculated by ηdyn =

Σk PP V · ∆T Pmax · ∆T

(11)

In this paper, the fastest irradiance variation for the two sequences are used to compare the tracking performance of

Number, n

Slope, W/m2 /s

Mode (t1 /t2 /t3 /t4 )

tini

Load, Ω

10 10

50 100

(8/10/8/10) (7/10/7/10)

30 30

80Ω 30Ω

A B

The experimental dynamic results are shown in Fig.21. According to EN 50530, the static and dynamic efficiency values are listed in TABLE VI. Fig.21 indicates that the P&O method is unable to track the MPP for either sequence A or sequence B. Although the VSSINC method performs good under sequence B under 1000W/m2 , it is unable to track the MPP under sequence A. Fig.21 shows that the proposed method outperforms the other methods under both of sequence A and sequence B. TABLE VI E XPERIMENTAL STATIC AND DYNAMIC EFFICIENCY RESULTS FOR EN 50530

MPPT methods P&O VSSINC Beta Proposed

Static efficiency 99.72% 99.77% 99.72% 99.84%

Dynamic efficiency sequence A sequence B 62.48% 94.32% 99.44% 99.76%

71.66% 97.73% 99.34% 99.91%



12


Power(W)

30

R EFERENCES

20 10 0 260

270

280

290

300

(a) P&O VSSINC Beta Proposed

Power(W)

60 40 20 0 80

Insulation and Power Equipment (EIPE15203), and the National Nature Science Foundation of China(51407145).

85

90

95 100 Time(s)

105

110

115

(b) Fig. 21. EN 50530 experimental results with P&O, VSSINC, Beta and the proposed method: (a)sequence A; (b)sequence B.

In summary, the experimental results show that the proposed method has the shortest tracking time, the lowest tracking power loss and the lowest steady-state power loss among these MPPT methods. VI. C ONCLUSION The paper presents a novel MPPT method, which is implemented through two major stages: a) Adaptive Scaling Factor Beta (ASF-Beta) to improve transient response; and b) Zero Oscillations Perturb and Observe (ZOPO) to eliminate steady-state errors. Various scenarios are analyzed including the irradiance variation and load variation conditions. Furthermore, according to EN50530, the static and dynamic MPPT efficiency measurements are performed with various MPPT methods. Both simulation and experimental results demonstrate the superior performance of the proposed algorithm over other MPPT methods. For instance, experimental results show that the overall tracking speed of the proposed method is 6 times, 4 times and 2 times faster than that of the P&O method, VSSINC method and conventional Beta methods, respectively. During the transient stage, the power loss is reduced by 20.83%, 14.26% and 6.53% in comparison with the P&O method, VSSINC method, and conventional Beta methods. Thanks to the ZOPO approach in minimizing steadystate oscillations, the power loss in steady state is 3 times lower than that of the P&O method and conventional Beta method, and 2 times lower than that of the VSSINC method. VII. ACKNOWLEDGEMENT This research was supported by the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (LAPS15014), the State Key Laboratory of Electrical

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Xingshuo Li was born in Zhengzhou, China. He received his B.S. in Computer Science from Zhengzhou University, Zhengzhou, China, in 2012, and M.S. in Sustainable Energy Technology with distinction from Xi’an Jiaotong-Liverpool University. He is currently working towards the Ph.D. degree at University of Liverpool, U.K. His research interests include digital control, power electronics, and power converters for Photovoltaic.

Huiqing Wen (M’13) received his B.S. and M.S. degrees in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2002 and 2006, respectively. In 2009, he received his Ph.D. in Electrical Engineering from the Chinese Academy of Sciences, Beijing, China. From 2009 to 2010, he has been an electrical engineer working with the GE (China) Research and Development Center Company, Ltd., Shanghai, China. From 2010 to 2011, he was an engineer at the China Coal Research Institute, Beijing, China. From 2011 to 2012, he was a postdoctoral fellow at the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. In 2013, he joined the Electrical and Electronic Engineering Department of Xi’an Jiaotong-Liverpool University (XJTLU), Suzhou, China. Currently, he is an associate professor at the XJTLU. His research interests include bidirectional DC-DC converter, power electronics in flexible AC transmission applications, electrical vehicles, and high-power, three-level electrical driving systems.

Lin Jiang received his B.S. and M.E. degrees from Huazhong University of Science and Technology, China, and his Ph.D. from the University of Liverpool, Liverpool, U.K., all in Electrical Engineering, in 1992, 1996, and 2001, respectively. He is a senior lecturer of Electrical Engineering at the University of Liverpool. His research interests include optimization and control of smart grid/electrical machine/power electronics and renewable energy.



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Weidong Xiao (M’07-SM’13) received the M.Sc. degree and Ph.D. degree from the University of British Columbia, Vancouver, Canada, in 2003 and 2007 respectively. He is currently associate professor with the department of electrical engineering and computer science at the Masdar Institute of Science and Technology, Abu Dhabi, UAE. In 2010, he spent eight months working as a visiting scholar at MIT, Cambridge, USA. Prior to the academic career, he worked with the MSR Innovations Inc. in Canada as a R&D engineering manager focusing on integration, research, optimization and design of photovoltaic power systems. His research interest includes photovoltaic power systems, dynamic systems and control, power electronics, and industry applications.

Yang Du received his Ph.D. in Electrical Engineering from The University of Sydney, Australia, in 2013. From 2013 to 2014, he was with Masdar Institute, Abu Dhabi, UAE, as a post-doctoral research fellow. Currently, he is a lecturer at Xian JiaotongLiverpool University, Suzhou, China. His research interests include power electronics application in photovoltaic systems, power quality issues caused by PV inverters, and reliability of power electronics converters.

Chenhao Zhao was born in Shaanxi, China. He received his B.S. degree in Electrical Engineering from Xi’an Jiaotong-Liverpool University, Suzhou, China. He is pursuing his M.S. degree at the University of Manchester, Manchester, U.K.. He is currently an assistant officer in the Department of Engineering and Physical Sciences, University of Manchester, Manchester, U.K.. His current research interests include power electronics and control, which include AC machine drives, and electric vehicles.
