Abstract
In order to improve maximum power point tracking (MPPT) performance, a variable and adaptive perturb and observe (P&O) method with current predictive control is proposed. This is applied in threephase threelevel neutralpoint clamped (NPC) photovoltaic (PV) generation systems. To control the active power and the reactive power independently, the decoupled power control combined with a space vector modulation block is adopted for threephase NPC inverters in PV generation systems. To balance the neutralpoint voltage of the threephase NPC gridconnected inverter, a proportional and integral control by adjusting the dwell time of small voltage vectors is used. A threephase NPC inverter rated at 12 kVA was established. The performance of the proposed method was tested and compared with the fixed perturbation MPPT algorithm under different conditions. Experimental results confirm the feasibility and advantages of the proposed method.
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1 Introduction
With increasing energy consumption, the importance of developing renewable energy sources is highlighted. Among different renewable energy sources, the photovoltaic (PV) energy source is considered one of the most promising clean energy sources because of its wide distribution and ease of utilization [1,2,3,4,5].
The curve for power versus voltage or power versus current of the PV array is nonlinear, and the output power of the PV array is dependent on irradiation as well atmospheric temperature. In order to realize the maximum utilization of the PV array, maximum power point tracking (MPPT) becomes of great significance in PV generation systems [6,7,8]. Recently, many MPPT algorithms have been presented, varying in structural complexity, control accuracy, response time, and cost. It is well known that the perturbation and observe (P&O) MPPT algorithm is the most popular because of its simple structure and control [6,7,8]. However, the conventional P&O method often suffers from some demerits. For instance, a large perturbation value will result in high PV array oscillations, while the dynamic response speed will be affected using a small perturbation value. Hence, a tradeoff between steadystate oscillation and fast response is generated for the conventional fixed perturbation P&O method. Another wellknown MPPT scheme is incremental conductance (INC), which achieves maximum power point (MPP) by comparing the INC of the PV array [9,10,11]. However, the INC method hardly achieves the real MPP in practical situations because of hardware limitations. To improve MPPT performance, an adaptive P&O MPPT technique based on a proportional and integral (PI) controller has been proposed [12]. This can achieve good steadystate and dynamic performance. However, this MPPT performance will heavily rely on the PI parameters, and the adjustment of PI parameters is difficult. Recently, intelligent control algorithms have been used to realize MPPT algoriths in distributed generation systems [13,14,15]. In [13], a fuzzy logic controller for MPPT was proposed. This achieves good steady and dynamic MPPT performance. However, the effectiveness of the fuzzy logic controller largely relies on the skill and experience of the designer. Similarly, an artificial neural network (ANN) intelligent algorithm was presented in [14, 15]. This exhibits perfect performance in MPPT, but it consumes a large computation time when implementing the MPPT algorithms with a digital signal processor (DSP).
In recent years, the implementation of digitally controlled techniques has been widely used in distributed generation systems, such as current predictive control, model predictive control (MPC), and model predictive power control [16,17,18,19,20,21,22,23,24]. Among different predictive methods, MPC has become very popular. MPC makes full play of limited switching states for power converters, and a cost function is employed to evaluate each switching state, and the switching state with minimum cost function will be selected and applied in the next control cycle. MPC can be applied in DC–DC converters and a fast response under irradiance change for MPPT has been achieved [18,19,20]. However, the MPC algorithm uses only one voltage vector in every switching period, and it needs high switching frequency to ensure performance improvement. Another method is current predictive control, which is essentially a digital control strategy and has been broadly employed in power electrics converters and motor drives [21,22,23,24]. In practical implementation, the duty ratio in the next switching cycle is directly calculated by the measured signals, the input and the output information. Compared with traditional PI control, current predictive control can realize better dynamic performance.
Inverters, considered as the bridge between generation systems and power grid or loads, are widely used. Compared with twolevel inverters, threelevel inverters have many advantages such as less total harmonic distortion (THD) of inverter output voltages, lower output filter size, and higher efficiency [25,26,27,28]. For threephase threelevel neutralpoint clamped (NPC) inverters, the most popular control strategy is voltageoriented control (VOC), which achieves decouple control for the active and reactive powers. However, its performance is largely dependent on the inner currentloop control [29, 30]. Another wellknown control strategy is called direct power control, in which the active power and the reactive power are directly regulated by the appropriate selection of a voltage vector from a switching table. Direct power control strategy has advantages of simple control and quick response, but the switching frequency is not fixed, which will result in difficult filter design [31, 32]. For threephase threelevel NPC inverters, one common question is how to balance the neutralpoint (NP) voltage. To regulate the NP voltage to half of the DClink voltage, different balancing control strategies have been proposed. These can be divided into hardware methods and software methods [33,34,35,36]. Hardware methods need extra hardware circuits to balance NP voltage, and this will increase the cost and size of the system. Software methods can mainly be classified into carrierbased pulse width modulation (CBPWM) and space vector PWM (SVPWM). Compared with the CBPWM method, the SVPWM method has many benefits, such as small NP voltage ripple and high DC voltage utilization [35, 36].
In this paper, a variable and adaptive P&O method with current predictive control is proposed. This is applied in threephase threelevel NPC gridconnected photovoltaic generation systems. The decoupled power control (DPC) combined with a space vector modulation (SVM) block is used and the NP voltage is well balanced by selecting proper small voltage vectors. A 12 kVA threephase NPC inverter prototype was built and a 32bit DSP (TMS320F2808) was adopted to realize the control strategy. Main experimental results were obtained for both the steadystate and dynamic responses to show the effectiveness of the proposed method.
2 PV generation systems and control strategy
2.1 PV generation configuration
A threephase threelevel NPC gridconnected photovoltaic generation system is depicted in Fig. 1. The PV generation system contains a PV array, a boost converter, threephase threelevel NPC inverters, an LC filter, and a power grid. In the PV generation systems, the PV array converts sunlight into electricity; the boost inverter is the power interface and achieves MPPT, and the threephase threelevel NPC inverter is employed to control the active power and the reactive power. In Fig. 1, V_{PV} and I_{PV} stand for input voltage and current of PV array; e_{a}, e_{b}, e_{c} are the grid voltages of phases a, b, and c, respectively; i_{a}, i_{b}, i_{c} are the inverter grid currents of phases a, b, and c, respectively; V_{p} and V_{n} represent the upper and lower DClink voltages; U_{DC} is the total DClink voltage; i_{N} is the NP current.
2.2 Implementation of current predictive control
The current predictive control method is to obtain the coming current value on the basis of the current predictive model, which is extensively used in power electronic converters. As shown in Fig. 1, when the boost converter switch S is turned on, the PV array current can be expressed as follows.
When the boost converter switch S is turned off, the boost converter voltage equation can be obtained as:
Applying a sampling period T_{s}, the derivative form dI_{PV}/dt can be approximated by:
Substituting (1) and (2) into (3), the relationships between the discretetime variables can be derived as:
The goal of current predictive control is to make the boost converter inductor current track the current reference. The boost converter inductance current waveform is displayed in Fig. 2. At the kth sampling instant in a sampling period T_{s}, the ontime of power switch S is assumed to be d(k)T_{s}, and the offtime of power switch S is considered to be (1 − d(k))T_{s}. Since the input PV array voltage V_{PV} and the output voltage DClink voltage U_{DC} are slowly changing compared with the sampling period, they can be considered as constant during a switching period. The boost converter inductor current I_{PV}(k + 1) at the (k + 1)th sampling period can be predicted using the input PV array voltage V_{PV}, the output voltage DClink voltage U_{DC}, the boost converter inductance L_{1}, the switching duty ratio d(k), and the switching period T_{s}. From (4), (5), and Fig. 2, the predictive current I_{PV} (k + 1) can be obtained as follows:
Solving (6), the predicted duty cycle can be obtained as:
The predictive boost converter current I_{PV}(k + 1) should follow the reference current \( I_{PV}^{*} \left( {k + 1} \right) \) at the next sampling period T_{s}. Therefore, the predicted duty cycle can be derived from (7) as:
The PV array current reference \( I_{PV}^{*} \left( {k + 1} \right) \) at the (k + 1)th sampling instant can be derived by applying a secondorder linear interpolation method, which can be given as:
where \( I_{PV}^{*} \left( {k  1} \right) \) is the PV array current reference at one previous sampling time; \( I_{PV}^{*} \left( {k  2} \right) \) is the PV array current reference at two previous sampling times.
2.3 MPPT control
As is well known, the powervoltage (PV) or currentvoltage (IV) characteristic of a PV array is nonlinear and shows one single MPP under normal operational conditions. For the conventional P&O algorithm, if the power change against the voltage change dP_{PV}/dV_{PV} of the PV string satisfies dP_{PV}/dV_{PV} > 0, the P&O scheme will make the PV array reference voltage operate in the same perturbation direction. If the perturbation voltage value in the previous time is positive or negative, the PV array reference voltage \( V_{PV}^{*} \) will increase or decrease. On the other hand, when the power change against the voltage change dP_{PV}/dV_{PV} of the PV array meets dP_{PV}/dV_{PV} < 0, the P&O method will make the PV array reference voltage work in the reverse perturbation direction. In this paper, a variable and adaptive P&O method with current predictive control is proposed, and the operation principle of the system is as follows:

1)
The PV string voltage V_{PV}(k) and string current I_{PV}(k) at the kth sampling period are measured by the PV array voltage sensor and PV array current sensor.

2)
The PV array power variation slowly changes and remains constant over the period of a sampling time. Therefore, a delay of 400 samples (20 ms) is used to produce two successive samples for the PV array power. This will reduce the computation burden for the MPPT algorithm [10]. The PV string power is calculated at the present sampling instant and the 400 previous sampling instants using the measured PV array voltage and current as follows:
$$ P(k) = V_{PV} (k)I_{PV} (k) $$(10)$$ P(k  400) = V_{PV} (k  400)I_{PV} (k  400) $$(11) 
3)
The power variation ΔP(k) of the PV string within the 400 sampling times (400T_{s}) can be obtained as:
$$ \Delta P(k) = P(k)  P(k  400) $$(12) 
4)
Calculate the PV array voltage reference using an adaptive and variable step method as:
$$ \begin{aligned} V_{ref} (n) = V_{ref} (n  1) + M\left {\frac{P(k)  P(k  400)}{{V_{PV} (k)  V_{PV} (k  400)}}} \right \hfill \\ = V_{ref} (n  1) + \Delta V_{ref} \hfill \\ \end{aligned} $$(13)where V_{ref} (n) is the present PV array voltage reference; V_{ref}(n − 1) is the previous PV array voltage reference; M is the step size. The perturbation voltage ΔV_{ref} can be given as:
$$ \Delta V_{ref} = M\left {\frac{P(k)  P(k  400)}{{V_{PV} (k)  V_{PV} (k  400)}}} \right $$(14)
From (14), it can be seen that the power change against the voltage change represents the irradiation change in terms of the PV curve of a PV array. If the irradiation change is small, the value of the power change against the voltage change is small. In the contrary case, the value will be large. When ΔV_{ref} is changing over a large range as a result of environmental variation, this algorithm will change ΔV_{ref} to a large value in order to realize fasttracking MPP. Once ΔV_{ref} is small, the MPPT algorithm assumes that the control system has reached the steadystate stage and ΔV_{ref} will be tuned to be small in order to make the power fluctuation small. Therefore, the disturbance step ΔV_{ref} of the MPPT algorithm is not fixed but adaptive according to environmental variation. This will improve MPPT efficiency. The flowchart of the variable and adaptive MPPT control is depicted in Fig. 3.
Because of its simple structure and high efficiency, the boost DC–DC converter is adopted to realize the MPPT algorithm in the system. For the proposed current predictive control, the control scheme of the adaptive and variablestep MPPT is illustrated in Fig. 4. Compared with conventional control, the proposed MPPT algorithm uses the current predictive control as the inner loop. The PI controller is employed as the outer loop for both methods. In the outer loop, the given voltage \( V_{PV}^{*} \) of the PV array is realized by the variable and adaptive MPPT control, and the difference between the given PV array voltage \( V_{PV}^{*} \) and the measured voltage V_{PV} is sent to the conventional PI controller. In the inner loop, the current reference \( I_{PV}^{*} \) of the PV string is set from the outer voltage PI controller, and the predicted duty cycle can be derived by the current predictive controller or the PI controller. A simple modulation generates the switching pulse of the boost converter.
2.4 NP voltage balancing for threephase NPC inverters
For threephase threelevel inverters, the operational status of each leg has three switching states, which can be represented by [P], [O], and [N]. Switching states of the inverter can use two pairs of complementary controlled power switches (S_{x1}, S_{x2}) and (S_{x2}, S_{x4}) for every phase x, where x can be a, b, and c. Switching state [P] means that the upper power switches (S_{x1}, S_{x2}) in Fig. 1 are turned on at the same time. Switching state [O] indicates that the middle power switches (S_{x2}, S_{x3}) are turned on at the same time, and switching state [N] demonstrates that the down switches (S_{x3}, S_{x4}) are on in the meantime. As shown in Fig. 1, switching state [P], switching state [O], and switching state [N] mean the inverter output voltage is + U_{DC}/2, 0 and − U_{DC}/2, respectively, when the NP defines the reference voltage. The threephase threelevel NPC inverter can generate 27 space voltage vectors. In terms of the magnitude of space voltage vectors, it can be divided into zero voltage vectors, small voltage vectors, medium voltage vectors, and large voltage vectors [33, 34]. For large voltage vectors, the NPC inverter outputs connect only to the positive DC rail or the negative DC rail, not to the NP. Therefore, large voltage vectors do not affect the NP voltage. For zero vector voltages, the inverter outputs simultaneously connect to the positive DC rail, the negative DC rail, or the NP, and also do not influence the NP voltage. For medium vector voltages, there is an inverter output connected to the NP, which will influence the NP voltage and will discharge or charge the DClink capacitors in terms of inverter output currents. For small vector voltages, at least one of the inverter outputs is connected to the NP. For the influence on the NP voltage, small vector voltages can be further classified as positive small vector voltages and negative small vector voltages. These output the same voltage but with opposite influence on the NP voltage. The voltage difference between the upper DClink voltage and the lower DClink voltage is defined as Δu_{d} =V_{p}−V_{n}. When the phase of the grid current i_{a} satisfies i_{a} > 0 in Fig. 1, the positive voltage vector [POO] will decrease the upper DClink voltage V_{p} and the voltage difference Δu_{d}, and the negative voltage vector [ONN[ will increase V_{p} and Δu_{d}. If the grid phase a current is i_{a} < 0, the upper DClink voltage V_{p} and the voltage difference Δu_{d} will operate in the opposite direction [35, 36]. From the above analysis, it can be concluded that small vector voltages come in pairs and each pair has an opposite influence on the NP voltage. Therefore, balancing the NP voltage is realized by choosing the appropriate small vector voltages. Assuming the total dwell time of a pair of small vector voltages is T_{total}, the dwell time of a positive small vector voltage is defined as:
From (15), the dwell time of the negative small vector voltage can be obtained as:
The control strategy for balancing the NP voltage is depicted in Fig. 5. The voltage difference Δu_{d} is sent to the PI controller, and the output of the PI controller regulates the value m according to the direction of the NP current i_{N}. The NP current i_{N} can be acquired by relationships between the inverter output currents and the switching states of the NPC inverters, and the NP current i_{N} will not be measured [35, 36]. If the voltage difference Δu_{d} is large, the PI output value m will also become large and the dwell time of the small vector voltage will be large. The result will be just the opposite when the value m is small. Therefore, the NP voltage is automatically adjusted.
2.5 Decoupled power control for NPC inverters
According to instantaneous power theory and coordinate transformation, the active power P and the reactive power Q for threephase threelevel inverters in the dq rotating reference frame can be obtained as [29]:
where e_{d} and e_{q} are the daxis and qaxis grid voltage in the dq rotating reference frame; i_{d} and i_{q} are the daxis and qaxis grid currents in the dq rotating reference frame.
Combined with SVM, the DPC strategy for the threephase threelevel NPC gridconnected inverter is described in Fig. 6. The special phase locked loop (PLL), called a ‘positive sequence detector (PSD)+dq−PLL’, which is free of grid voltage harmonics, is widely used in distributed generation systems [37]. Therefore, it is employed in this paper. To reduce the harmonic currents of the NPC inverter currents caused by loworder harmonics in grid voltages, the grid voltage feedforward control is used [37]. The NPC inverter has to realize two goals. The first goal is to stabilize the DClink voltage, and the second is to transform active and reactive powers to the power grid under different irradiation in photovoltaic generation systems. From Fig. 6, it can be seen that the control scheme contains two loops. The outer loop is a DClink voltage loop for stabilizing the DClink voltage, and the inner loop is a power loop for tracking the given powers. The measured DClink voltage U_{DC} subtracts the reference DClink voltage \( U_{\text{DC}}^{*} \), and the error is sent to a conventional PI controller. The active power reference P^{*} can be acquired after the output signal of the DClink PI controller multiplying the measured DClink voltage U_{DC}. The reactive power reference Q^{*} can be set in terms of the requirements of power systems, which can be set to absorb reactive power from the power grid or to send reactive power to the power grid. The active and reactive power errors between the power references and the calculated powers are sent to power PI controllers. The daxis voltage reference \( u_{d}^{*} \) can be obtained after an output signal from the active power PI controller adding the daxis grid voltage e_{d}. In the same way, the qaxis voltage reference \( u_{q}^{*} \) is calculated as the output of the reactive power PI controller plus qaxis grid voltage e_{q}. With the help of the PSD+dqPLL method, the daxis voltage references \( u_{d}^{*} \) and the qaxis voltage references \( u_{q}^{*} \) can be transformed into the αaxis voltage references \( u_{\alpha }^{*} \) and the βaxis voltage references \( u_{\beta }^{*} \) through coordinate transformation. The output 12pulse signals for the threephase NPC inverter, which determine the current states of the power switches, can be acquired by the SVM algorithm using the αaxis voltage references \( u_{\alpha }^{*} \), the βaxis voltage references \( u_{\beta }^{*} \), and the output of balancing the NP voltage PI controller.
3 Experimental results
3.1 Experimental test bench and parameters
To further validate the feasibility and correctness of the proposed control strategy, an experimental block diagram based on the TI 32bit DSP (TMS320F2808) is used and shown in Fig. 7. The inverter output currents and PV array current are acquired by a VAC current sensor 4646X400, and the upper DClink voltage, the lower DClink voltage, PV array voltage, and grid phase voltages are sampled by an LEM voltage sensor LV25P. The current and voltage signals are sent to a 12bit DSP internal analog to a digital (A/D) port. A complex programmable logic control device (CPLD) expands the PWM pulse signals generated by the TMS320F2808 chip. A power module is used as a leg for the threephase threelevel inverter. The experimental parameters are listed in Table 1. To simulate PV array characteristics, a programmable DC source Topcon Quadro 32K is used. This can change the PV array curve through a monitored interface.
In the experiment, three PV string curves are used. For the first PV string, the main PV array parameters are set as opencircuit voltage V_{oc1}=650 V, shortcircuit current I_{sc1}=13.5 A, and MPPT voltage V_{MPPT1}=520 V. The second curve is set with main parameters of V_{oc2} = 650 V, I_{sc2}=27 A, and V_{MPPT2}=520 V, and the third curve is set at V_{oc3} = 750 V, I_{sc3}=8 A, and V_{MPPT3} = 600 V.
3.2 MPPT

1)
Steadystate performance of MPPT
In the steadystate test, the DClink voltage reference \( U_{\text{DC}}^{*} \) is given as 620 V, and the reactive power reference Q^{*} is set to zero in order to achieve a unity power factor. The proposed MPPT algorithm shown in Fig. 4 is evaluated on the established experimental bench for different conditions. In Fig. 4, a PI controller is employed when implementing the fixed P&O MPPT method, and different perturbation values are used. In addition, the current predictive controller is used when realizing the proposed MPPT. Figure 8 shows the experimental waveforms of the fixed P&O MPPT method and the proposed MPPT method. Comparative experimental waveforms of phase a grid voltage e_{a}, phase a grid current i_{a}, PV string voltage V_{PV}, and PV string current i_{PV} for different MPPT algorithms are depicted in Fig. 8 with the first PV array input. Figures 8a and b show the results by using the P&O MPPT method, and their perturbation values are 0.5 V and 3 V. Figure 8c shows the results using the proposed MPPT scheme. Figure 8 shows that the oscillation amplitudes in the PV array voltage and PV array current are small for the three different methods. Specifically, when the inverter operates at MPP using different algorithms, the variation of the PV output voltage is measured at less than 5 V and the corresponding oscillation of the PV output power is measured at less than 4 W. Thus, the static performance using these three methods are almost the same.

2)
Transient performance of MPPT
The dynamic behavior of MPPT schemes has been examined under different conditions:
Case 1: Suddenly stepping input PV array from the first curve to the third curve.
The proposed MPPT method is compared with the conventional fixed P&O MPPT scheme, which has two different fixed perturbation values, 0.5 V and 3.0 V for transients. To simulate sudden irradiation changing conditions, the DC power source can be set by loading different PV array curves. Figure 9 depicts phase a grid voltage e_{a}, phase a grid current i_{a}, PV string input voltage V_{PV}, and PV string input current I_{PV} for different MPPT schemes under the Case 1 condition. From Fig. 9, it can be seen that 11 s are needed to reach steadystate using 0.5 V fixed perturbation value, 9.92 s for 3 V fixed perturbation value, and only 7.60 s for the proposed MPPT scheme, which indicates that the proposed MPPT scheme has a faster tracking speed because of a variable and adaptive step. In Fig. 9, the PV array voltage reaches steadystate without fluctuations for the proposed MPPT scheme, while the PV array voltage uses the P&O method with fixed perturbation value oscillations for a long period before reaching the steadystate MPP. The larger the fixed perturbation value adopted, the greater the PV array voltage oscillations before reaching the steadystate MPP. As observed from Fig. 9 in the dynamic response, it can be concluded that the proposed MPPT scheme has better transient response than the fixed perturbation value method. This will improve MPPT efficiency especially for dynamic tracking.
3.3 Threephase NPC inverters results
To validate the feasibility of the DPC control strategy for the NPC inverter, the dynamic behavior is studied. Experimental dynamic study of NPC inverters has been carried out under different conditions:
Case 2: Suddenly stepping the input PV string from the first curve to the second curve.
Case 3: Suddenly stepping the input PV string from the second curve to the first curve.
Aiming to realize the unity power factor for the NPC inverter, the reactive power reference Q^{*} is set to zero. Figure 10 shows experimental waveforms of the phase a grid voltage e_{a}, the phase a grid current i_{a}, the phase b grid current i_{b} and the NP oscillation voltage Δu_{d} in the different cases. Figure 10a and b display the dynamic performance under Case 2 and Case 3, respectively. As observed in Fig. 10, phase a grid current i_{a} is perfecly sinusoidal, and the total harmonic distortion (THD) of phase a grid current i_{a} is only 3.8%, which is measured by a power analyzer under the second PV array. The THD of phase a grid current i_{a} is less than 5%, which meets the national grid standard when distributed generation systems are connected to a power grid through power electronic converters.
From Fig. 10, it is seen that the NP oscillation voltage Δu_{d} is less than 15 V (only 2.4% of rated voltage) in the steadystate operation and less than 30 V (only 5.0% of rated voltage) in the dynamic operation. This validates the effectiveness of the NP balancing control for the threelevel NPC inverter. As shown in Fig. 10, it is also concluded that the phase a grid current is in line with the phase a grid voltage in the steadystate test and even in the dynamic test and the power factor is 0.994 measured by a power analyzer under the second PV array. This means that the active power and the reactive power are successfully decoupled using DPC control with SVM. From the dynamic response in Fig. 10, it is found that the phase a grid current of the NPC inverter can reach steadystate in less than 3 ms under a step change, which is 50% of the rated power change, and rarely occurs in practical photovoltaic generation systems. These experimental waveforms indicate that the proposed control strategy achieves excellent steadystate and dynamic response for the threephase NPC inverter.
4 Conclusion
This paper presents an adaptive P&O and current predictive MPPT algorithm with decoupled power control applied in threephase NPC gridconnected inverters. The conventional fixed perturbation MPPT method and proposed method are compared in both steadystate operation and dynamic response. The results show that the proposed MPPT scheme has good steadystate and dynamic performance. The variation of the PV output voltage of the proposed MPPC method is less than 5 V and the proposed MPPT has faster dynamic MPPT performance than traditional methods. The proposed method only needs 7.6 s after getting the MMP in the dynamic process. The two other, traditional, methods require 9.92 s and 11 s. In addition, decoupled control for active power and reactive power is also achieved with good steadystate and dynamic performance. The NP balancing scheme with the PI controller is very effective in balancing the NP voltage, and the NP oscillation voltage is less than 15 V in steadystate operation and less than 30 V in dynamic operation. However, the proposed current predictive MPPT control does not consider inductance change in the boost inverter, and the deviation value in the current predictive model will influence MPPT accuracy. Therefore, current predictive MPPT control under inductance change will be studied further in future.
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Acknowledgements
This work was supported in part by the National Young Natural Science Foundation of China (No. 51407124), in part by China Postdoctoral Science Foundation (No. 2015M581857), and in part by Suzhou prospective applied research project (No. SYG201640).
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CrossCheck date: 13 June 2018
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YANG, Y., WEN, H. Adaptive perturb and observe maximum power point tracking with current predictive and decoupled power control for gridconnected photovoltaic inverters. J. Mod. Power Syst. Clean Energy 7, 422–432 (2019). https://doi.org/10.1007/s405650180437x
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DOI: https://doi.org/10.1007/s405650180437x