Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions
Abstract
:1. Introduction
- (1)
- The output characteristics of the PV arrays are analyzed using the PV array model under PSC, and the V–P curve is found to demonstrate a multi-peak trend. The reasons for the failure of the conventional MPPT algorithm are analyzed under the premise of rapid and continuous irradiance changes.
- (2)
- For the MPPT failures caused by the timings of the irradiance changes, this paper proposes a hybrid MPPT method that uses an artificial neural network (ANN) to estimate the MPP and an augmented state feedback precise linearization (AFL) controller for the DC/DC converter to meet the fast and frequent changes in irradiance.
- (3)
- Considering the influence of the multi-peak output of the PV array on the small signal of the DC/DC converter under PSC, this paper designs a nonlinear control method with precise state feedback linearization.
2. Grid-Connected PV Generation System
2.1. Structure of the Proposed System
2.2. PV Array Model under PSC
2.3. Failure Analysis of GMPPT under PSC
- (1)
- Assuming that the illumination characteristic of the PV array at the moment t is given by the L3–R3 curve, and that the lighting condition changes at moment t + 1, the output characteristic curve of the PV array becomes L1–R1, and the actual PV output becomes S1. As the PV curve exhibits a multi-peak shape, the traditional MPP R1 cannot be obtained by searching the LMPP L1 using the gradient information as in the P & O and INC methods. Some experts found that the overall output power of the PV array changed greatly in this process. Global search algorithms such as the particle swarm optimization (PSO) algorithm or the artificial bee colony (ABC) algorithm can be used for global optimization, by using the amplitudes of the output power variations and the t + 1 global optimal solution R1 to solve the local shadow problems of the PV output characteristics with multiple peaks.
- (2)
- The light characteristic curve of the PV array is assumed to be the L1–R1 curve at moment t, and the curve of the PV characteristic becomes L3–R3 at moment t + 1, which indicates that the MPP of the PV system should change from R1 to L3.
3. ANN Method for Maximum Power-Point Tracking (MPPT)
3.1. Neural Network Construction for MPPT
3.2. Neural Network Analysis for MPPT
4. Topology and Control Strategy for Proposed Power Converter
4.1. Nonlinear Model of DC/DC Converter
4.2. Augmented-State Feedback Linearization (AFL) Control for Nonlinear Systems
4.3. DC/AC Inverter and Control
5. Digital Simulation Experiments and Analysis
5.1. Simulation Case 1
5.2. Simulation Case 2
- (1)
- As shown in Part I of Figure 14, when the shading condition changes to SP2 from SP1, the PV output characteristic changes from the pink curve to the brown curve. The traditional P & O algorithm (the green curve in Figure 14) can track the MPP (point a) in section SP1. However, only the local MPP (point b) in section SP2 can be tracked by the traditional P & O algorithm, which indicates that the traditional P & O algorithm for MPPT fails to track the GMPP in section SP2. Since the instantaneous power change ΔP is large, the improved P & O algorithm (the blue curve in Figure 14) can start the global search module and track the GMPP (point c), similar to the method proposed in this paper (the red curve in Figure 14). It is clear from the dynamic process that the response time of the proposed method is much less than that of the improved P & O algorithm, and that the tracking speed is increased more than 6-fold. By combining this inference with the information in Table 3, it can be inferred that the steady-state maximum power of the proposed method is also superior to that of the improved P & O algorithm.
- (2)
- When the shading condition changes to SP2 from SP3, the PV output characteristic changes from the brown curve to the black curve, as shown in Figure 14II. It can be seen that the MPP (point c) of the SP2 shading condition is near the local MPP (point d) of the SP3 shading condition. It is difficult to start the global search because the power change due to the shading condition change is not large enough. Therefore, the improved P & O and traditional P & O algorithms track the local MPP (point d) in identical manners, which indicates that the GMPP tracking fails in the cases of the improved P & O and traditional P & O algorithms. It can be seen from Table 3 that the power loss caused by MPPT failure is 699 W, which accounts for approximately 10% of the maximum power. The method proposed in this paper can track the MPP (point e) quickly and accurately, and effectively solve the MPPT failure problem caused by local shadow conditions.
6. Conclusions
- (1)
- The PV output characteristics were modeled and analyzed under PSC, and the complex nonlinear multi-peak morphology of the PV array output was verified. It was found that the timings of irradiance changes might cause the failure of traditional MPPT methods or make it difficult to define the starting conditions, especially for MPPT algorithms based on voltage or current information.
- (2)
- Based on the above analysis, an artificial neural training network model was designed based on environmental variables and irradiance information, and GMPPT was realized efficiently and effectively using the hybrid method (ANN + AFL) for the DC/DC converter. A comparison of the proposed MPPT method with the conventional P & O method and the improved P & O method was illustrated through simulations. The GMPPT failure caused by the timing of the irradiance change was solved.
- (3)
- For the problems caused by the partial shading process, such as the MPP voltage of the PV output being shifted greatly, the static operating point of the system being changed, or the difficulty of designing a PI controller to eliminate the steady state under small-signal modeling, this paper proposed an AFL control method for nonlinear systems to accurately track the MPP without static errors. The control parameters were clear and easy to design and apply.
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Nonlinearity Control Theory and Parameter Analysis in Third-Order Systems
A.1. Some Definitions in Nonlinearity Control Theory
A.2. Multi-Input Feedback Linearization Theorem
- (i)
- a nonsingular state feedback:
- (ii)
- a local diffeomorphism in V0: ,if, and only if, in U0:
- (i)
- , is involutive and of constant rank.
- (ii)
- , Rank Gn−1 = n.
Appendix B. Description of the Detailed Model
B.1. Simulation Parameters
B.2. Simulation Model in Matlab/Simulink
Abbreviations
C1, C2 | parameters of the PV panels under standard test conditions (STCs) |
Vpv | PV substring voltage |
Ipv | PV substring current |
Iapv | PV array current |
Vapv | PV array voltage |
Papv | PV array power |
Iscn | short-circuit current |
Vocn | open-circuit voltage |
Im | MPP current |
Vm | MPP voltage |
Ns | number of PV modules in series |
Np | number of PV modules in parallel |
Gi | PV cells irradiance |
γj, λij | weights |
bj, c | biases for each joint from the input layer to the output layer |
Pm | MPP power |
Vdc | DC-link voltage |
ed, eq | d–q components of the grid voltage |
id, iq | d–q components of the output current |
pdc | DC-link power |
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Parameter | Value |
---|---|
Voc (open-circuit voltage) | 65.2 V |
Isc (short-circuit current) | 5.96 A |
Vm (MPP (maximum power point) voltage) | 54.7 V |
Im (MPP current) | 5.58 A |
Pm (MPP power) | 305.2 W |
Section No. | Time (s) | Shading Pattern [G1,1~12, G2,1~12, G3,1~12, G4,1~12, G5,1~12, G6,1~12] (W/m2) |
---|---|---|
SP1 | 0.1~0.3 | [300, 300, 300, 1000, 700, 700] |
SP2 | 0.3~1.5 | [300, 300, 300, 1000, 500, 500] |
SP3 | 1.5~2.0 | [300, 300, 300, 1000, 1000, 300] |
Section No. | Ideal Maximum Power (W) | Output Power Obtained (W) | ||
---|---|---|---|---|
P & O | Improved P & O | ANN + AFL 1 | ||
SP1 | 8393.4 | 8282.9 | 8283.1 | 8381.4 |
SP2 | 7341.3 | 5989.2 | 7225.3 | 7311.2 |
SP3 | 7811.6 | 7108.4 | 7112.6 | 7798.8 |
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Chen, M.; Ma, S.; Wu, J.; Huang, L. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Appl. Sci. 2017, 7, 95. https://doi.org/10.3390/app7010095
Chen M, Ma S, Wu J, Huang L. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Applied Sciences. 2017; 7(1):95. https://doi.org/10.3390/app7010095
Chicago/Turabian StyleChen, Mingxuan, Suliang Ma, Jianwen Wu, and Lian Huang. 2017. "Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions" Applied Sciences 7, no. 1: 95. https://doi.org/10.3390/app7010095
APA StyleChen, M., Ma, S., Wu, J., & Huang, L. (2017). Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Applied Sciences, 7(1), 95. https://doi.org/10.3390/app7010095