A Phase-Shift-Modulated LLC-Resonant Micro-Inverter Based on Fixed Frequency Predictive-MPPT

: Maximum Power Point Tracking (MPPT) control is an essential part of every photovoltaic (PV) system, in order to overcome any change in ambient environmental conditions and ensure operation at maximum power.. Recently, micro-inverters have gained a lot of attention due to their ability to track the true MPP for each individual PV module, which is considered a powerful solution to overcome the partial shading and power mismatch problems which exist in series-connected panels. Although the LLC resonant converter has high e ﬃ ciency and high boosting ability, traditional MPPT techniques based on Pulse Width Modulation (PWM) do not work well with it. In this paper, a ﬁxed frequency predictive MPPT technique is presented for the LLC resonant converter to be used as the ﬁrst-stage in a PV micro-inverter. Using predictive control enhances the tracking e ﬃ ciency and reduces the steady state oscillation. Operation with ﬁxed switching frequency for the LLC resonant converter improves the total harmonic distortion proﬁle of the system and ease the selection of circuit magnetic component. To demonstrate the e ﬀ ectiveness of the proposed MPPT technique, the system is simulated using MATLAB / Simulink platform. Furthermore, a 150 W hardware prototype is developed and tested. Both simulation and experimental results are consistent and validate the proper operation of the developed system.


Introduction
Photovoltaic (PV) cells are one of the promising kinds of renewable energy. The compound annual growth rate (CAGR) of PV installations was 36.8% between the years 2010 to 2018 [1,2]. It is worth noting that the annual installation of PV stations in 2017 alone was the same as the total PV capacity until the end of 2012 [3]. It is expected that renewable power capacity will continue to increase by 50% between 2019 and 2024 [4]. PV systems have different classifications, but they could be classified according to grid integration into [5][6][7]: (1) Stand-alone PV systems (off-grid), and (2) Grid-connected PV systems.
in off-grid PV systems, in order to feed essential loads during emergencies [8]. There are different categories of storage systems like lead acid batteries. For example, the usage of supercapacitors is a good solution in case of limited energy storage capacity [9]. On the other hand, when the storage station is not able to cover all load demands, a hybrid system can represent a good solution [10]. Hybrid system using PV generation and hydrogen energy storage system is presented in [11].
In grid integrated PV systems, the PV panels are connected to the grid via a DC/AC converter. The grid voltage is fixed, and hence, the PV system is working as a current source which is injecting a sinusoidal current into the grid. The different formations which are developed in the literature for grid-tied PV systems are summarized as follows: (i) Centralized PV arrays, where a huge number of PV panels are connected in series and parallel configuration and then they are connected to a centralized DC/AC converter. This configuration is commonly used in very high power PV plants. However, this system requires expensive switches and high voltage wiring [12], and in case of partial shading or mismatches, the system fails to extract the maximum power [12,13].
(ii) Multi-string inverter. This configuration is used in medium power PV power plants. Strings are connected in parallel and each group of the parallel string is connected to their own DC-DC converter. All these converters are connected to the utility grid through a central DC/AC converter. Partial shading problems have less effect than in the centralized formation case, however as it still depends on a centralized inverter, inverter failures can shut down the whole plant [13].
(iii) Micro-inverter. This configuration is well suited for low power PV applications, where each PV panel has its own DC/AC converter [14][15][16]. Such a formation overcomes partial shading and power mismatch problems. Due to their compactness and high efficiency, micro-inverters have gained a lot of attention in grid-tie applications [17][18][19]. The main advantage of using a micro-inverter is that each PV module has its own power conversion, and hence independent MPPT control. Consequently, a global MPPT system is not required, as each PV module is operating at its maximum power in an independent way. Micro-inverters can be classified into single-stage micro-inverters and two-stage microinverters [20]. Two stage micro-inverters consist of DC-DC converters to perform voltage boosting and MPPT extraction and DC-AC converter to convert the DC voltage into AC voltage, while single stage micro-inverters consist of only one stage that performs voltage boosting, MPPT tracking and converts the DC voltage into AC voltage.
The general structure of a micro-inverter is illustrated in Figure 1. The general requirements of micro-inverters include the ability to operate at high efficiency, high power density and operation over a wide range of dynamic load changes [21]. The first stage of a micro-inverter is constituted by a DC-DC converter. Different types of DC-DC converters are described in the literature, but the high frequency (HF) resonant converter has small-size magnetic components, galvanic isolation, and higher efficiency over a wide load range. Such features make resonant converters a perfect choice for micro-inverter applications. Soft switching techniques are applied to the resonant converter to improve the overall system efficiency and reduce the switching losses of the system. Micro-inverter topologies can be classified into isolated micro-inverters and non-isolated micro-inverters. In non-isolated micro-inverters, the configuration does not include any transformer and the DC/DC stage is used such as boost, buck-boost or cuk converters [22][23][24]. Isolated micro-inverters include a transformer, high frequency or line frequency transformer, such as current-feed push-pull [25,26], flyback converters [27,28], matrix converters [29,30] and resonant converters [31][32][33][34]. Converters operating in soft switching mode are preferred more than hard-switching converters. Hard-switching causes higher switching losses, lower efficiency and damage to the switching devices. Resonant converters represent a superior solution for PV applications due to their high efficiency and zero-voltage switching (ZVS) and/or zero-current switching (ZCS) operation [35,36] MPPT proposed in [37] with an enhancement of the ordinary INC method by predicting the error before applying the switching signal. In [38], a variable-frequency fixed-step P&O predictive control method was implemented with a good dynamic response and small power ripple at steady state, while a variable step size sensorless predictive MPPT was proposed in [39]. In [40], a predictive MPPT is presented for a Z-source grid-connected inverter using variable frequency control. All the previously mentioned techniques are implemented for PWM converters, but none of them could be applied directly to resonant topologies. Due to the nonlinearity of the voltage gain versus frequency relationship, MPPT with a special design mast be considered for frequency-modulated LLC resonant converters. Most of the old MPPT methods have been modified to be compatibile with different resonant converters. A modified P&O for a resonant converter is presented in [41,42]. Although this method is easy, it has some limitations that can be summarized as: fixed-step P&O delays the response of the system, and the long tracking time leads to an increase in power losses.
In [43] a fixed step P&O variable frequency control method is proposed for the LLC resonant converter. Although it is a simple technique, it suffers from a long transient period. A variable step variable frequency MPPT control is implemented in [44], but it suffers from a wide range of harmonics and bigger EMI, due to its variable frequency operation. Also, the design of the magnetic component is a cumbersome operation; a phase-shift fixed-frequency modulation control is used to overcome those disadvantages [44,45]. The use of fixed-frequency modulation with the LLC resonant converter is first addressed in [46,47], which use a fixed-frequency P&O MPPT but with high steady state oscillation.
Energies 2020, 13, x FOR PEER REVIEW 3 of 15 while a variable step size sensorless predictive MPPT was proposed in 39]. In [40], a predictive MPPT is presented for a Z-source grid-connected inverter using variable frequency control. All the previously mentioned techniques are implemented for PWM converters, but none of them could be applied directly to resonant topologies. Due to the nonlinearity of the voltage gain versus frequency relationship, MPPT with a special design mast be considered for frequency-modulated LLC resonant converters. Most of the old MPPT methods have been modified to be compatibile with different resonant converters. A modified P&O for a resonant converter is presented in [41,42]. Although this method is easy, it has some limitations that can be summarized as: fixed-step P&O delays the response of the system, and the long tracking time leads to an increase in power losses.
In [43] a fixed step P&O variable frequency control method is proposed for the LLC resonant converter. Although it is a simple technique, it suffers from a long transient period. A variable step variable frequency MPPT control is implemented in [44], but it suffers from a wide range of harmonics and bigger EMI, due to its variable frequency operation. Also, the design of the magnetic component is a cumbersome operation; a phase-shift fixed-frequency modulation control is used to overcome those disadvantages [44,45]. The use of fixed-frequency modulation with the LLC resonant converter is first addressed in [46] and 47], which use a fixed-frequency P&O MPPT but with high steady state oscillation. This manuscript presents a novel fixed-frequency phase-shift (FFPS) predictive MPPT for LLC resonant converters to be used in the two-stage micro-inverter configuration for grid-tied PV applications. This manuscript modifies the content developed in 48], where the system is briefly discussed and only simple simulation results are included. On the other hand, here complete hardware results are presented, as well as an extensive system analysis.
The proposed fixed frequency predictive MPPT for LLC resonant converters has several advantages over other MPPT techniques suitable to be applied for tLLC resonant converters, which are as follows: 1) small steady state error due to the use of a PI controller. 2) Fast transient performance due to the prediction of reference voltage, and 3) simple parameter design due to the usage of fixed frequency modulation.The developed two-stage micro-inverter schematic is shown in Figure 2. It is constructed from a LLC resonant converter and an h-bridge inverter. This manuscript considers only the DC-DC part. The choice of the LLC resonant converter, the first stage in the proposed system, comes from its distinct features over other resonant converter topologies such as the ability to operate at ZVS/ZCS, wide input-voltage range, step-up ability, and high efficiency.
This paper is organized as follows: Section 2 discusses the analysis of LLC resonant DC/DC converter, then Section 3 discusses the proposed MPPT technique using the predictive Fixed-Frequency phase-shift control, Section 4 presents the simulation results for the proposed MPPT technique and experimental results, and finally Section 5 presents the experimental validation of the proposed MPPT technique.

Analysis of the LLC Phase-Shift Modulated Resonant Converter
The LCC resonant converter depicted in Figure 2 consists of s phase-shift switching network, resonant tank, high frequency transformer, and voltage doubler. The switching network depends on the voltage gain requirements, and it may be constructed from a half-bridge or full-bridge. The switching network chops the input DC voltage into high-frequency square pulses. The resonant network consists of a series of Ls and Cs , and Cp in parallel with the rectifier input. The energy applied This manuscript presents a novel fixed-frequency phase-shift (FFPS) predictive MPPT for LLC resonant converters to be used in the two-stage micro-inverter configuration for grid-tied PV applications. This manuscript modifies the content developed in [48], where the system is briefly discussed and only simple simulation results are included. On the other hand, here complete hardware results are presented, as well as an extensive system analysis.
The proposed fixed frequency predictive MPPT for LLC resonant converters has several advantages over other MPPT techniques suitable to be applied for tLLC resonant converters, which are as follows: (1) small steady state error due to the use of a PI controller. (2) Fast transient performance due to the prediction of reference voltage, and (3) simple parameter design due to the usage of fixed frequency modulation.The developed two-stage micro-inverter schematic is shown in Figure 2. It is constructed from a LLC resonant converter and an h-bridge inverter. This manuscript considers only the DC-DC part. The choice of the LLC resonant converter, the first stage in the proposed system, comes from its distinct features over other resonant converter topologies such as the ability to operate at ZVS/ZCS, wide input-voltage range, step-up ability, and high efficiency.
This paper is organized as follows: Section 2 discusses the analysis of LLC resonant DC/DC converter, then Section 3 discusses the proposed MPPT technique using the predictive Fixed-Frequency phase-shift control, Section 4 presents the simulation results for the proposed MPPT technique and experimental results, and finally Section 5 presents the experimental validation of the proposed MPPT technique.

Analysis of the LLC Phase-Shift Modulated Resonant Converter
The LCC resonant converter depicted in Figure 2 consists of s phase-shift switching network, resonant tank, high frequency transformer, and voltage doubler. The switching network depends on the voltage gain requirements, and it may be constructed from a half-bridge or full-bridge. The switching network chops the input DC voltage into high-frequency square pulses. The resonant network consists of a series of L s and C s , and C p in parallel with the rectifier input. The energy applied across the resonant tank by the switching network is circulated through the resonant tank network. Applied energy is delivered to the output either in the same or the next switching cycle.
The gating signal and key waveforms of the LLC resonant converter are shown in Figure 3. The converter is analyzed based on the fundamental harmonic approximation (FHA) technique given in [44]. The equivalent phasor circuit of the LLC converter is illustrated in Figure 4. The DC-input voltage is converted to a square wave waveform by the switching network. The output of the switched network appears between X and Y terminals. The root mean square (RMS) value of the fundamental component of the AC voltage V XY is given by: where δ is the pulse width angle. it has an angle complementary to the phase shift angle α and α = π − δ as shown in Figure 2. By using high switching transformer with turns ration n, the RMS value of primary voltage V Lp can be obtained as: Then from (1) and (2): Referring to the phasor equivalent circuit of the converter in Figure 4, the following relation can be obtained: Thus from (3) and (4), the converter voltage gain M can be obtained by (5) as follows: where: L s C s , and R ac = ( 8 π 2 )R l . f s refers to the switching frequency, and f r : is the resonant frequency. V o (ac) is the RMS of the output voltage. V xy1 is the r.m.s. value of the output voltage of the inverter across terminals XY. R l is the load resistance referred to primary-side.

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Applied energy is delivered to the output either in the same or the next switching cycle.
The gating signal and key waveforms of the LLC resonant converter are shown in Figure 3. The converter is analyzed based on the fundamental harmonic approximation (FHA) technique given in 44]. The equivalent phasor circuit of the LLC converter is illustrated in Figure 4. The DC-input voltage is converted to a square wave waveform by the switching network. The output of the switched network appears between X and Y terminals. The root mean square (RMS) value of the fundamental component of the AC voltage VXY is given by:

DC-AC Converter
where δ is the pulse width angle. it has an angle complementary to the phase shift angle α and α=πδ as shown in Figure 2. By using high switching transformer with turns ration n, the RMS value of primary voltage can be obtained as: Applied energy is delivered to the output either in the same or the next switching cycle. The gating signal and key waveforms of the LLC resonant converter are shown in Figure 3. The converter is analyzed based on the fundamental harmonic approximation (FHA) technique given in 44]. The equivalent phasor circuit of the LLC converter is illustrated in Figure 4. The DC-input voltage is converted to a square wave waveform by the switching network. The output of the switched network appears between X and Y terminals. The root mean square (RMS) value of the fundamental component of the AC voltage VXY is given by:

DC-AC Converter
where δ is the pulse width angle. it has an angle complementary to the phase shift angle α and α=πδ as shown in Figure 2. By using high switching transformer with turns ration n, the RMS value of primary voltage can be obtained as: Then from (1) and (2):  Referring to the phasor equivalent circuit of the converter in Figure 4, the following relation can be obtained: Thus from (3) and (4), the converter voltage gain M can be obtained by (5) as follows:

Proposed Fixed-Frequency Phase-Shift Modulated MPC-MPPT Control
Unlike the previously mentioned works, this manuscript presents a novel fixed frequency predictive maximum power point technique with an adaptive step-size for a phase-shift modulated LLC resonant converter. The schematic of the control feedback system is depicted in Figure 5.
The operation of the proposed methodology is performed in four steps, as follows: Step 1: The PV terminals voltage value V PV (K), may be increased or decreased, depending on the applied switching state, during the next sampling time (K+1), And hence the next sampling time of PV voltage V PV (K+1) is defined as: where ∆V is the step size. This step size could be set as a fixed value or could be designed to be variable according to change in the power level. A variable step size could be defined from the following equation: where σ is normalizing weigh factor, which is tuned to get good steady state performance by trial and error, P max (K + 1) is the next sampling time predicted maximum extracted PV power, the steps for calculating the value of P max (K + 1) will be explained in this section later. However, at starting an initial value of ∆V can be set. Step 2: The next sampling time of the PV terminals voltage ( + 1) and the PV current ( + 1) are predicted. In order to reduce the number of sensors, a digital observer is used. Figure. 6 presents the equivalent circuit of PV module using the Thevenin theorem. Designed digital observer is presented to calculate the required equivalent voltage ( ) and the equivalent resistance ( ) as foellows: Then the next sampling time predicted PV current can be calculated as: Step 3: Next the predicted next sampling time PV that can be extracted from the PV is calculated as follows: Step 2: The next sampling time of the PV terminals voltage V PV (K + 1) and the PV current I PV (K + 1) are predicted. In order to reduce the number of sensors, a digital observer is used. Figure 6 presents the equivalent circuit of PV module using the Thevenin theorem. Designed digital observer is presented to calculate the required equivalent voltage (Veq) and the equivalent resistance (Req) as follows: Energies 2020, 13, 1460 7 of 16 Then the next sampling time predicted PV current can be calculated as: Step 3: Next the predicted next sampling time PV that can be extracted from the PV is calculated as follows: is presented to calculate the required equivalent voltage ( ) and the equivalent resistance ( ) as foellows: Then the next sampling time predicted PV current can be calculated as: Step 3: Next the predicted next sampling time PV that can be extracted from the PV is calculated as follows: V eq Figure 6. The Thevenin equivalent circuit of the PV module.
After calculating all possible output power of each switching state, during the next sampling time. Maximum power could be calculated as: Step 4: Then the cost function can be evaluated as: After calculating all possible output power of each switching state, during the next sampling time. Maximum power could be calculated as: Step 4: Then the cost function can be evaluated as: After evaluation of the cost function by the proposed FFPS predictive MPPT to track the maximum available power from the PV, a reference voltage will be chosen for the next sampling period, that the larger value of cost function will be the next sampling time target, as example, if the cost function J 1 is greater than J 2 , the PV voltage must be shifted to V PV (k + 1) 1 , else if J 2 is greater than J 1 so the PV reference voltage will be V PV (k + 1) 2 . PI controller is added to track the measured PV voltage with the predicted reference voltage. Prediction of the reference voltage improves the transient performance of the system, while using PI controller to track the reference voltage improves the steady state performance of the system.

Simulation Results
The operation of the proposed predictive MPPT technique is validated using a 300 W MATLAB/ Simulink model. The input voltage was changed over a wide range from 25 V to 41 V. The resonant frequency F r is selected to be 140 kHz, while switching frequency is set to 154 kHz. The resonant parameters are set to 4.1/3415 µH/nF for the resonant inductor and resonant capacitor, respectively. The transformer turns ratio is 1:7. The PV module used in the simulation has maximum power characteristics (9.6 A/31.25 V). In order to demonstrate the superior behavior of the proposed technique, different operating condition are taken into account. Figure 7 illustrates a case of study of using fixed step-size, the irradiation level is set to 100% at the start, then, at time t = 0.7 s, a reduction of the radiation level to 50% is applied as shown in Figure 7a. The proposed technique can extract maximum power. Figure 7b,c shows the change of the phase-shift to track the maximum power. parameters are set to 4.1/3415 μH/nF for the resonant inductor and resonant capacitor, respectively. The transformer turns ratio is 1:7. The PV module used in the simulation has maximum power characteristics (9.6 A/31.25 V). In order to demonstrate the superior behavior of the proposed technique, different operating condition are taken into account. Figure 7 illustrates a case of study of using fixed step-size, the irradiation level is set to 100% at the start, then, at time t = 0.7 s, a reduction of the radiation level to 50% is applied as shown in Figure 7a. The proposed technique can extract maximum power. Figure 7b,c shows the change of the phase-shift to track the maximum power.  Another case study is taken into account where a variable step-size FFPS predictive MPPT is considered. The results are depicted in Figure 8. The solar irradiation is shown in Figure 8a, the power extracted from the PV panel is shown in Figure 8b, as it is indicated in Figure 8c the oscillation around the MPPT is reduced with oscillations of less than ±1%.
Another simulation case study is depicted in Figure 9, where the solar irradiation was changed from 100% to 30% and then back again to 100% (Figure 9a). As can be seen from Figure 9b, the FFPS predictive MPPT technique is able to extract the maximum power at all different conditions. The phase shift variation for this case study is depicted in Figure 9c. Another case study is taken into account where a variable step-size FFPS predictive MPPT is considered. The results are depicted in Figure 8. The solar irradiation is shown in Figure 8a, the power extracted from the PV panel is shown in Figure 8b, as it is indicated in Figure 8c the oscillation around the MPPT is reduced with oscillations of less than ±1%. Another simulation case study is depicted in Figure 9, where the solar irradiation was changed from 100% to 30% and then back again to 100% (Figure 9a). As can be seen from Figure 9b, the FFPS predictive MPPT technique is able to extract the maximum power at all different conditions. The phase shift variation for this case study is depicted in Figure 9c.

Experimental Results
A laboratory prototype for the LLC resonant converter with its proposed FFPS Predictive MPPT technique was implemented. A general schematic for the hardware layout is depicted in Figure 10. It consists of a LLC resonant converter, TMS320F2835 DSP controller kit, and resistive load, in addition

Experimental Results
A laboratory prototype for the LLC resonant converter with its proposed FFPS Predictive MPPT technique was implemented. A general schematic for the hardware layout is depicted in Figure 10. It consists of a LLC resonant converter, TMS320F2835 DSP controller kit, and resistive load, in addition to the PV terminals. A JWP 250 PV module is used and the key parameters of the prototype hardware are listed in Table 1.

Experimental Results
A laboratory prototype for the LLC resonant converter with its proposed FFPS Predictive MPPT technique was implemented. A general schematic for the hardware layout is depicted in Figure 10. It consists of a LLC resonant converter, TMS320F2835 DSP controller kit, and resistive load, in addition to the PV terminals. A JWP 250 PV module is used and the key parameters of the prototype hardware are listed in Table 1.    Different study cases have been investigated in the laboratory for the proposed FFPS predictive MPPT for the LLC resonant converter, and one of these cases is depicted in Figure 11. In this study case, the available maximum power from the real system is 100 W. As can be seen from the graph, the proposed algorithm is efficiently able to extract the 100 W with efficiency around 99%. The steady state oscillation for the proposed phase-shift MPPT technique is illustrated in Figure 12, where it is shown the power oscillates around the MPP within a ±0.5 W range. Different study cases have been investigated in the laboratory for the proposed FFPS predictive MPPT for the LLC resonant converter, and one of these cases is depicted in Figure 11. In this study case, the available maximum power from the real system is 100 W. As can be seen from the graph, the proposed algorithm is efficiently able to extract the 100 W with efficiency around 99%. The steady state oscillation for the proposed phase-shift MPPT technique is illustrated in Figure 12, where it is shown the power oscillates around the MPP within a ±0.5 W range.    Another experimental case study is depicted in Figure 13. In this study case, the available maximum power from the real system is 115 W. As can be seen from the graph, the proposed algorithm is efficiently able to extract the 115 W effectively. Another experimental case study is depicted in Figure 13. In this study case, the available maximum power from the real system is 115 W. As can be seen from the graph, the proposed algorithm is efficiently able to extract the 115 W effectively. To prove the validity of the proposed MPPT technique under partial shading conditions and abrupt change in solar radiation conditions, a partial shading test and abrupt change in solar radiation test are performed, illustrated in Figure 14 and Figure 15. In the partial shading case of study, depicted in Figure 14, a part of the real PV module is under lower radiation comditions. The radiation level and the maximum monitored available power were found to be 55 W. As the figure demonstrates, the proposed MPPT algorithm extracts the real maximum power from the module with low oscillation and small transient time. Figure 15 depicts a case study where there is a sudden change in the solar radiation level, where the proposed MPPT technique able to track the maximum power with low oscillation and small transient time. A two-step test is performed and the result is shown in Figure 16, where partial shading conditions are formed by shading a part of the PV module, then this shading is removed, and as shown in the figure, the proposed fixed-frequency predictive MPPT effectively tracks the MPP.
The turn-on ZVS is indicated in Figure 17. During turning on the switch, its current should be To prove the validity of the proposed MPPT technique under partial shading conditions and abrupt change in solar radiation conditions, a partial shading test and abrupt change in solar radiation test are performed, illustrated in Figures 14 and 15. In the partial shading case of study, depicted in Figure 14, a part of the real PV module is under lower radiation comditions. The radiation level and the maximum monitored available power were found to be 55 W. As the figure demonstrates, the proposed MPPT algorithm extracts the real maximum power from the module with low oscillation and small transient time. Figure 15 depicts a case study where there is a sudden change in the solar radiation level, where the proposed MPPT technique able to track the maximum power with low oscillation and small transient time. A two-step test is performed and the result is shown in Figure 16, where partial shading conditions are formed by shading a part of the PV module, then this shading is removed, and as shown in the figure, the proposed fixed-frequency predictive MPPT effectively tracks the MPP. radiation level and the maximum monitored available power were found to be 55 W. As the figure demonstrates, the proposed MPPT algorithm extracts the real maximum power from the module with low oscillation and small transient time. Figure 15 depicts a case study where there is a sudden change in the solar radiation level, where the proposed MPPT technique able to track the maximum power with low oscillation and small transient time. A two-step test is performed and the result is shown in Figure 16, where partial shading conditions are formed by shading a part of the PV module, then this shading is removed, and as shown in the figure, the proposed fixed-frequency predictive MPPT effectively tracks the MPP.
The turn-on ZVS is indicated in Figure 17. During turning on the switch, its current should be negative by passing through the switch body diode. So that the switch capacitance is discharged and ZVS is achieved.     The turn-on ZVS is indicated in Figure 17. During turning on the switch, its current should be negative by passing through the switch body diode. So that the switch capacitance is discharged and ZVS is achieved. Figure 16. Proposed Fixed-Frequency Predictive MPPT operation waveforms under partial shading condition (two-step step down then step up in the irradiation) ) (Ch2 (green) is PV voltage, Ch4 (pink line) is the PV current), the PV extracted power (lavender line ).

Conclusions
This manuscript has presented a fixed frequency predictive-MPPT for phase-shift modulated LLC resonant converters for PV applications. Design steps for the control algorithm with the LLC resonant converter have been presented in a comprehensive way. The proposed FFPS predictive MPPT achieved the maximum available power from the PV module with an efficiency around 99% and steady state oscillation around ±0.5 W @ 115 W. The proposed fixed frequency predictive MPPT

Conclusions
This manuscript has presented a fixed frequency predictive-MPPT for phase-shift modulated LLC resonant converters for PV applications. Design steps for the control algorithm with the LLC resonant converter have been presented in a comprehensive way. The proposed FFPS predictive MPPT achieved the maximum available power from the PV module with an efficiency around 99% and steady state oscillation around ±0.5 W @ 115 W. The proposed fixed frequency predictive MPPT for LLC resonant converters demonstrated several advantages over other MPPT techniques suitable to be applied to LLC resonant converters such as: (1) a small steady state error due to the use of a PI controller. (2) Fast transient performance due to prediction of the reference voltage, and (3) a simple parameter design due to the usage of fixed frequency modulation. A 300 W simulation model was implemented, then a 250 W hardware step-up was tested. Both simulation and hardware results are consistent and proved the high performance of the proposed predictive MPPT algorithm for LLC resonant converters.