Duty-Cycle Predictive Control of Quasi-Z-Source Modular Cascaded Converter Based Photovoltaic Power System

A duty-cycle predictive control is proposed for dc grid integration of front-end isolated quasi-Z-source modular cascaded converter (qZS-MCC) photovoltaic (PV) power system. The post-stage qZS half-bridge dc-dc converter deals with PV maximum power point tracking, dc grid integration, and dc-link voltage balance; whereas, the front-end isolation converters operate at a constant duty cycle of 50%. Thus, it saves control hardware resources while overcoming challenges from PV-panel voltage variations and dc-bus voltage limit. The proposed control uses the derived circuit model to predict the global active-state duty cycle for grid-connected current control and predict the shoot-through duty cycles for dc-link voltage balance, achieving a fast and accurate tracking target. The proposed control method has advantages of: i) eliminating weighting factors that exist in conventional model predictive control (MPC), ii) no sophisticated loop parameters design that exists in proportional-integral (PI) control, iii) operating at constant switching frequency that is different from the conventional MPC with variable switching frequency. Simulation and experimental tests are carried out to verify the effectiveness of the proposed control method and compare with the PI-based control system.


I. INTRODUCTION
Nowadays, the ever-increasing installed capacity of the largescale photovoltaic (PV) power plants locate in remote areas, which usually have abundant irradiation. Therefore, accommodating high voltage (HV) dc transmission can lower power loss [1]. Conventional solutions commonly use a central inverter with a bulky step-up transformer or the cascaded multilevel inverter, in order to invert the dc voltage from the PV panels into a HV ac bus [2]- [4]. The high ac voltage is then converted to a high dc voltage for the long-distance transmission. A decoupling inverter is further required to recover the ac voltage from the high dc voltage, to match the utility The associate editor coordinating the review of this manuscript and approving it for publication was Firuz Zare. grid or load. Such multistage conversion, i.e., dc-ac-HV ac-HV dc-ac, encounters challenges of cost, efficiency, and power density [5].
Considering the natural dc characteristics of PV power, motivations have been concentrated toward dc collection of PV power at the distribution level, forming the configuration of dc-HV dc-ac [6]- [8]. Due to the limit on insulation voltage of commercial PV panels which is normally 1.5 kV, galvanic isolation is normally required to protect the PV panels. For those purposes, the quasi-Z-source modular cascaded converter (qZS-MCC) with dc integration of PV power is proposed in [7]- [12]. The qZS-MCC is formed by front-end isolated qZS half-bridge (HB) PV submodules (SMs), which isolates the PV panels from HV side of qZS-MCC. Thus, it overcomes the insulation voltage limit of PV panels. With cascaded structure on the dc output of qZS-HB SMs, a high dc-bus voltage is directly obtained. It is workable to extend the operation power scale with multi qZS-MCC PV systems parallelly tied to the dc collection grid to expand the power simply at utility scale. In addition, inherited from the characteristics of quasi-Z-source inverter (qZSI) [13]- [18], the post-stage qZS-HB dc-dc converter is able to deal with PV maximum power point tracking (MPPT) and dc-link voltages balance. Hence, only a unified and constant 50% duty cycle is applied to the front-end isolation converters of all SMs, without any extra control efforts needed. Therefore, hardware resources and costs can be significantly saved, especially in cases with numbers of SMs, compared to its counterparts which are consisted of two-stage isolated dc-dc converters [19]- [21].
System-level control method of the qZS-MCC PV power system has been developed, using 2n+1 proportional-integral (PI) control loops for n SMs formed qZS-MCC [10], [12]. In the previous work, each SM needs a dual-loop PI regulatorbased shoot-through (ST) duty cycle control to balance the dc-link voltages, and one extra PI regulator-based PV panel voltage control to track the MPPT, while a PI regulator controlling the dc grid-connected current. Whereas, design of PI-based control is a tough task, especially for multi-loop PI controls, because sophisticated controller parameters design based on system transfer functions and Bode plots is usually needed, to play with tradeoff between stability and transient optimization [22]- [26]. In addition, stability and rapidity of the PV power system are highly dependent on PI parameters. Derivative regulator could be combined to improve the performance, but it also increases the design complexity [27].
Various contributions have been dedicated to the control of traditional qZSI power systems. To improve the dynamic responses with respect to PI-based control, the non-linear fuzzy logic control [28], neural network control [29], sliding mode control (SMC) [30]- [33], and model predictive control (MPC) [34]- [39] were developed. Among them, the SMC and MPC were paid high attractions due to the simple implementation through digital controllers [40], [41]. Besides that, the MPC has accurate tracking capability to the reference, fast dynamic responses to condition changes, and is insensitive to circuit parameters variations. The conventional MPC predicts the qZS-network capacitor voltage and inductor current, as well as output current for the next control cycle; then evaluates the defined cost function at all the switching states in the present control cycle; the one corresponding with the minimum value of cost function is selected as the switching state of the next control cycle. Whereas, variable switching frequency is introduced, which causes difficulty in cooling system and filter design [39]. Furthermore, high performance is at the expense of high computation burden, due to the fact that the number of switching states increase exponentially with the increase of power devices' number, such as the qZS-MCC with numbers of SMs in cascade, while all the states have to be evaluated within one control cycle [42]. A discrete-time average model-based predictive control was proposed for the three-phase qZSI by predicting the ST duty cycle and modulation waves [43], and a dead-beat control was developed to estimate the modulating waves of a three-phase rectifier [44], whereas, only constant dc/ac voltage source and standalone loads are discussed. The qZS-MCC PV power system has to consider also the system-level control functions, such as PV MPPT, dc grid integration, dc-link voltage balance, and cascaded voltage output.
This article proposes a duty-cycle predictive control for the qZS-MCC PV power system, featuring a comprehensive controller design with simple implementation while maintaining fast and accurate tracking capability. The ST duty cycles for dc-link voltage balance and total active-state duty cycle for dc grid power injection are predicted through the derived discrete-time models and feedbacks in real time, while a PI regulator of each SM tracks MPPT of PV panels. In the proposed control, no parameter design efforts are needed in the predictive loop, thus, the controller design is much simplified when compared to PI-based control. The predicted control variables are provided to the qZS-MCC modulator, thus switching control signals with constant switching frequency are fulfilled. The prediction process is executed once in each control cycle based on the derived predictive models, rather than evaluating a cost function for all available switching states, so the computation burden is significantly reduced when compared with the conventional MPC method. That benefit is especially critical for a number of SMs cascaded qZS-MCC.
The paper is structured as follows: Section II introduces the qZS-MCC PV power system; Section III details the proposed predictive control of the system, including grid-connected current, MPPT, and dc-link voltage control; Section IV illustrates simulation and experimental results, and comparison results with the PI-based control of qZS-MCC, followed by the conclusion in Section IV. Fig. 1 shows the topology of qZS-MCC for dc collection of PV power. HB formed SMs are cascaded to increase output voltage. An isolated HB converter is inserted into the front end of each SM to isolate the PV panel from the high voltage grid. Hence, the qZS-MCC can achieve a voltage much higher than PV panel's insulation voltage. Several qZS-MCC PV systems can be simply integrated at the high-voltage dc bus [9], [11].

II. QZS-MCC PV POWER SYSTEM
A qZS network, consisted of two inductors, two capacitors, and one diode, is embedded into the post stage of HB SM. In one control period T s , each qZS-HB SM possesses the ST state and non-ST state. The latter includes active state and traditional zero state. Fig. 2 shows the equivalent circuit of poststage qZS-HB SM, illustrated by SM 1 . As shown in Fig. 2 (a), when the ST occurs, both post-stage switches S b11 and S b12 turn on, the dc-link voltage v DC1 is zero. From Fig. 2 (b), during the active state of non-ST state, the upper switch S b11 is on while the lower one S b12 is off; the output voltage v o1 is high with the amplitude of dc-link peak voltage V DC . In the  zero state of non-ST state, the anti-parallel diode of S b12 freewheels and the output voltage v o1 becomes zero.
The qZS-HB does not contribute to the output voltage in the zero and ST states. Then the qZS-MCC's output voltage is summarized as And its average dc value is where S k ∈{0, 1} denotes the switching function of the kth SM's post-stage HB, V DCk denotes the dc-link peak voltage of the kth SM, V ok denotes the average dc output voltage of the kth SM, and M k denotes the active-state duty cycle of the kth SM, k ∈{1, . . . , n} denotes the SM number.
The kth SM's dc-link peak voltage, and voltages of capacitors C 1 and C 2 are, respectively [25]  where D k denotes the ST duty cycle of the kth SM, and v ink denotes the qZS-network input voltage from the HB isolated converter of the kth SM. Inherited from qZS converters and through regulating the ST duty cycle in (3), the post-stage qZS-HB is able to handle variations of the input voltage v ink . A high-frequency transformer with 1:1 turn ratio is combined with the front-end HB switches, S fk1 and S fk2 , to achieve voltage isolation. When a constant duty cycle D 0 = 0.5 is used, the output voltage is doubled [11]. Namely, there are This design can achieve benefits as follows: i) isolation between PV panel and high voltage grid; ii) PV voltage boost; iii) the maximum utilization of the HB isolated converter [11]; iv) low size of transformer; v) simple control implementation due to constant duty cycle of 0.5. Fig. 3 shows the block diagram of proposed control method for the qZS-MCC based high-voltage PV power system. The control targets include MPPT of isolated PV arrays, SMs' dc-link voltage balance, and power injection into dc collection grid. As Fig. 3

III. PROPOSED DUTY-CYCLE PREDICTIVE CONTROL OF QZS-MCC PV POWER SYSTEM
where V DC = V DC1 = V DC2 =. . . = V DCn denotes the constant dc-link peak voltage of all SMs, v G denotes the dc grid voltage, L F denotes filter inductance, and R E denotes internal resistance. When any SM is in zero or ST states, there is As shown in Fig. 4 (a), there is a 180 • phase difference between carriers v Carr1 and v Carr2 of the two SMs. Use v Carr1 as reference. In one control cycle, the current increments are i o1 [N ] and i o2 [N ] , respectively, in t 1[N ] and t 2[N ] durations, due to the charging action of filter inductor when both SMs are in the active-state duty cycle. Therefore, the total Similarly, for n SMs, the sum of active-state duty cycles in the N th control cycle is noted as With (5) and (6), the derivation of grid-connected current with respect to the current increment and decrement durations are expressed as, respectively, Using Euler method, the discrete current derivation holds From (7) and (8), the average grid-connected current in one control cycle will be Hence, through (9), it can be derived that From (10) and Fig. 4 (b), at the end of the N th control cycle, i.e., the beginning of the (N +1)th control cycle, the gridconnected current is controlled to i o[N +1] through M T [N ] . Therewith, at the end of the (N +1)th control cycle, the current i o[N +2] can be obtained as from the effort of at the end of the N th control cycle. The cost function of VOLUME 8, 2020 grid-connected current control for the N th control cycle is defined as When the control is well worked, the grid-connected current i o[N +1] tracks well with the reference current where I * o[N ] denotes the reference grid-connected current. Substituting (10) and (13) into (11), the global active-state duty cycle for the (N +1)th control cycle can be predicted by 2

) DUTY CYCLE DISTRIBUTION FOR MPPT
As the proposed control shown in Fig. 3, the error between actual post-stage qZS-HB input voltage v ink and reference voltage v * ink is compensated by a PI regulator in each SM, acquiring the maximum point power P * k of the kth SM. In order to inject the maximum point power of each SM into the dc collection grid, the predicted global active-state duty cycle M T [N +1] for the next control cycle is distributed to the kth SM's active-state duty cycle where P * T = P * 1 + P * 2 + . . . + P * n denotes the sum of n SMs' maximum point powers.
Due to the constant 50% duty cycle of the front-end isolation converter, the qZS-HB input voltage v ink and current i ink are measured to perform the perturbation and observation MPPT, obtaining the reference voltage v * ink of the kth SM. Furthermore, to interface with the dc collection grid and inject all the collected PV power into the grid, the reference grid-connected current in (12) is determined by Hence, the predictive control and distribution of global active-state duty cycle and the PI-based input voltage control achieve the grid-connected current control and PV MPPT.

B. DC-LINK VOLTAGE BALANCE CONTROL
Each SM's post-stage qZS-HB operates independently at its own ST and non-ST states, according to the on-off states of switches S bk1 and S bk2 . In the ST state, the PV panel and qZS capacitors charge the qZS inductors, therefore, the qZS inductor currents increase while qZS capacitor voltages decreasing. In the non-ST state, the PV panel and qZS inductors charge the qZS capacitors and provide power to the load, with qZS inductor currents decreasing and qZS capacitor voltages increasing.
Under L 1 = L 2 = L and C 1 = C 2 = C, dynamic equation of the kth SM's qZS network is simplified as a second-order system [45], [46]. In the ST state, there are where r and R denote the internal resistance of qZS inductor and capacitor, respectively. The non-ST state yields where where D k [N ] denotes the kth SM's ST duty cycle in the N th control cycle. From (21) and (22), the qZS inductor current i ink[N +1] and capacitor voltage v C1k[N +1] at the end of N th control cycle can be derived. Therewith, the qZS-HB input current i ink and capacitor-C 1 voltage v C1k at the end of (N +1)th control cycle can be obtained by 172738 VOLUME 8, 2020 The control objective of ST duty cycle D k [N ] is to ensure a zero tracking error between the reference dc-link peak voltage V * DCk[N +1] and the actual peak voltage V DCk[N +1] , besides a zero error between the reference qZS-HB input current I * ink[N +1] and actual current i ink [N +1] , at the end of N th control cycle. Then, the cost function of dc-link voltage control for the kth SM is defined as Similar to the derivation of grid-connected current control, there is g k[N +1] = 0 through the effort of D k[N +1] at the end of the (N +1)th control cycle, when the control is well operated. Taking into account much small sampling time and from (3), there are Substituting (26) into (24) and (27) into (23), respectively, the reference qZS-HB input current I * ink [N ] can be obtained by And with the i ink[N +1] and v C1k[N +1] from (21) and (22), the D k[N +1] for the next control cycle is predicted by where Then, at the identical dc-link voltage references ] , all the n SMs' dc-link peak voltages will be balanced for the (N +1)th control cycle, even though the PV panel voltage varies.

C. IMPLEMENTATION AND ADVANTAGES
According to Fig. 3, the steps to implement the proposed duty-cycle predictive control of qZS-MCC system are shown as follows.
i) At the beginning of the N th control cycle, the gridconnected current i o [N ] is measured to predict the global active-state duty cycle M T [N +1] through (14), for the (N +1)th control cycle.
ii) With the PI-based MPPT control, the active-state duty cycle M k[N +1] of the kth SM is obtained through (15).
iii) The kth SM's qZS-HB input current i ink [N ] and qZS capacitor-C 1 voltage v C1k [N ] are measured to predict the ST duty cycle D k[N +1] of the kth SM by (29), for the (N +1)th control cycle. If M k[N +1] is higher than the carrier, S bk1 is ON, otherwise, it is OFF, and S bk2 is completely opposite to S bk1 .
It can be seen that the proposed control applies one PI regulator and one predictive loop of each SM, as well as one predictive loop of the system current control, i.e., n PI regulators and n+1 predictive loops of the control system. Table 1 shows the controller design, computation, and parameters of the proposed, PI-based, and conventional MPC methods. Comparing to the latter two, the advantages of proposed control are listed as follows.
i) The cost function is defined to zero, as a result that there is no cost function calculation required in the proposed control method. It overcomes the disadvantage of the conventional MPC that needs to calculate a cost function in each control cycle. According to the conventional MPC, the more the cascaded SMs, the heavier the computation burden, which grows exponentially with the switching devices. Therefore, the computation effort is much reduced for the qZS-MCC using the proposed control.
It should be highlighted that the cost function of conventional MPC causes the two main issues: first, it is hard to choose best weighting factors for the cost function because there is no theory to support its design, and trial and error method is the only way; second, sometimes the chosen weighting factors may cause a stability issue at some operation conditions and its reliability and robustness are concerns. These disadvantages are the main challenges for the conventional MPC in application to the qZS-MCC because immense weighting factors are needed. The proposed control fully overcomes these issues.
ii) The proposed control predicts the duty cycles of the next control cycle to achieve the control goals through the modulator, as shown in Fig. 5. As a result, a constant switching frequency is achieved. This avoids disadvantage of the conventional MPC that has a variable switching frequency. It can be seen that the switching frequency of the proposed control method is controlled as needed. A high switching frequency will reduce the size of passive components, such as QZS inductors and capacitors and filter inductor, but switching power loss will be increased. A small switching frequency will lower the switching power loss, but increase passive components size.
iii) The controller design and implementation are much simple because there are no controller parameters required in the predictive control loops. For instance, no weighting factors as the conventional MPC or proportional and integral parameters as the PI-based control are involved.
Each SM has one PI regulator only for achieving MPPT in the proposed control. This PI regulator can be designed by employing typical Bode plot design method [14]. In addition, the SMs' PI and predictive control are independently implemented. Therefore, a modular and scalable design will be easily realized for the qZS-MCC when numbers of SMs are cascaded to achieve a high voltage.

IV. SIMULATION AND EXPERIMENTAL INVESTIGATIONS
A qZS-MCC PV system consisted of two front-end isolated qZS-HB SMs is built. The proposed duty-cycle predictive control is implemented and compared with the conventional PI-based control of the qZS-MCC PV system.
To make the comparison of the two methods under the same condition, the qZS inductance and capacitance values and PI regulator's parameters of MPPT control in simulation and experiment are selected according to those in [10] and [12], where the qZS inductance is designed to limit the peakto-peak switching frequency ripple of qZS inductor current within 20% and the qZS capacitance is to buffer the peakto-peak switching frequency ripple of dc-link peak voltage within 1%. Table 2 lists the simulation and prototype parameters. Table 3 lists the controller parameters of the PI-based control. Fig. 6 (a) shows a high-level schematic of the experimental system, and Fig. 6 (b) shows the experimental setup. Each SM's qZS-network inductors are built on the coupled AMCC-250 core. The TMS320F28335 based digital signal processor (DSP) control board performs the proposed control method. As shown in Fig. 6, the front-end HB of SM 1 and SM 2 share one PWM register that the same signal    In the investigations, simulation and experimental tests are firstly carried out for the proposed duty-cycle predictive control of the qZS-MCC PV system. The two SMs operate at the same condition at the beginning. A sudden irradiance increase from 600 W/m 2 to 1000 W/m 2 is applied to the SM 1 's PV panel at 0.5 s in simulation. In the experimental tests, the PV panels of two SMs are working at 25 • C and 600 W/m 2 at the beginning; then the irradiance of SM 1 increases to 1000 W/m 2 by regulating solar array simulator. Results shown in Figs. 7 and 8, respectively. For the comparison, the PI-based control of qZS-MCC in [10], [12] is tested on the built prototype. Similar condition of sudden irradiance increase is performed to SM 1 from 600 W/m 2 to 1000 W/m 2 , as results shown in Fig. 9.  v DC1 recovers to the starting value after a short adjusting time, while that of SM 2 remaining unchanged. In consequence, the peak value of qZS-MCC output voltage v o maintains the same, as Figs. 7 (d) and 8 (d) show, regardless of the PV panel voltage variation in SM 1 .
Also, from Fig. 7 (c), it can be seen that the active-state duty cycle M 1 of SM 1 increases and that of SM 2 decreases, which handles the power difference between the two SMs. In addition, from the increased grid-connected current i o and unchanged qZS-MCC output voltage v o of Figs. 7 (d) and 8 (d), it can be obtained that the increased PV power of SM 1 caused by irradiance rising is injected into dc collection grid.
It is noted that the proposed predictive control achieves fast and accurate tracking for the qZS-MCC, with simple control structure and controller design. The circuit voltages and currents of qZS-MCC become stable with a fast response speed after the irradiance change, while a constant switching frequency is achieved, as the voltages of the two SMs' power devices shown in Fig. 7 (e).

2) RESULTS OF PI-BASED CONTROL METHOD
For PI-based control, in each SM, there is one PI regulator based MPPT control adjusting the PV panel voltage, and one dual-loop control, consisted of a PI regulator and a proportional regulator, balancing the dc-link peak voltages. Besides, one PI regulator controls global grid-connected current. Controller parameters are as shown in Table 4. Fig. 9 shows results of two SMs' PV panel currents and voltages, two SMs' qZS-HB input currents and voltages, two SMs' dc-link voltages, as well as grid-connected current and qZS-MCC output voltage, corresponding to those of predictive control in Fig. 8.
From experimental results of Figs. 8 and 9, it can be seen that both methods demonstrate good steady-state stability that the MPPT is well achieved, the dc-link peak voltages are balanced, and the increased PV power is injected into the dc collection grid, even though there are PV panel current and voltage variations. Whereas, the qZS-MCC system shows smaller overshoots and much faster response speed from the proposed predictive control than the PI-based control. From Figs. 8(c) and (d) and 9(c) and (d), the grid-connected current and two SMs' dc-link peak voltage have smaller overshoots under the proposed control than using the PI-based control. It can be seen that the overshoot of SM 1 's dc-link voltage v DC1 and qZS-MCC output voltage v o are ignorable, and the currents and voltages become stable within 50 ms, when applying the proposed predictive control. However, a 7.8-V overshoot appears on v DC1 , and nearly 500 ms settling time appears to circuit currents and voltages when using the PI-based control.

B. DISCUSSION
From the control block diagram of the proposed duty-cycle predictive control in Fig. 3 and the control block diagram of PI-based control shown in [12], it can be seen that both methods have 2n+1 control loops. The PI-based control needs to elaborately design 4n+2 proportional and integral parameters and n proportional parameters through specific small-signal modeling and transfer function derivation. Whereas, more than half PI regulators design related efforts are eliminated in the proposed predictive control. The n+1 predictive loops of the proposed control obtain the control variables of ST duty cycles and active-state duty cycles through the derived discrete-time circuit model, without need of tough PI parameters design.
From Figs. 7-9, it can be seen that both methods achieve accurate steady-state stability of circuit voltages and currents. Whereas, the dynamic responses of qZS-MCC system are much faster when using the proposed control than with PI-based control. In addition, the proposed control method shows high robustness, even though the duty-cycle predictive model involves circuit parameters.
Moreover, less design parameters in the proposed control method also simplifies the design, which enhances the system reliability. The grid-connected current and qZS-MCC output voltage are tested when a wide irradiance change from 400 W/m 2 to 1000 W/m 2 is applied to SM 1 . In the tests, all the other controller parameters of the two methods are kept same as the tested condition in Figs. 8 and 9. Fig. 10 (a) and (b) shows results from the proposed predictive control and PI-based control, respectively. It can be seen that the proposed predictive control still shows smaller overshoots and much faster response speeds than that of the PI-based control in this case. Furthermore, comparing Figs. 8 (d) with 10 (a), and 9 (d) with 10 (b), it can be seen that the proposed predictive control achieves similar response speed and overshoot to the grid-connected current VOLUME 8, 2020 and qZS-MCC output voltage with the test in Fig. 9. Whereas, larger overshoots and worse response waveforms appear to the current and voltage in Fig. 10 (b) than those in Fig. 9 (d), indicating potential instability of PI regulators when a wider irradiance change occurs.
In summary, the proposed duty-cycle predictive control simplifies the control design and implementation, while improving the performance of the qZS-MCC PV power system in terms of much fast dynamics and high robustness.

C. PARAMETER VARIATIONS
The parameters of passive components, such as qZS-network inductors and capacitors and grid filer inductor, tend to vary, which would result into parameters mismatch between the SMs.
Investigations are carried out on parameters varying of the grid-side filter inductance L F , qZS-network inductance L, and qZS-network capacitance C in the circuit, while all parameters remaining unchanged in the predictive controller. The ±50% variations from the normal values are conducted on the passive component parameters. Fig. 11 (a) shows the grid-connected current ripple ratio, from the peak-to-peak ripple current to the average current, versus passive component parameters variations. It can be seen that the variations of the grid-side filter inductance has dominant effect than other components. And variations of qZS-network inductance and capacitance have little effects on the grid-connected current ripple. In all cases, the current ripple ratio is almost within 10%, which is absolutely safe from the 20% design criteria, even at the ±50% variations.
The dc-link voltage ripple ratio, from the peak-to-peak ripple voltage to the average value of dc-link voltage, versus different qZS-network capacitance between the two SMs is also investigated. Fig. 11 (b) shows the results, where r vDC1 and r vDC2 denote the dc-link voltage ripple ratios of SM 1 and SM 2 ; C 11 and C 21 denote the capacitance of qZS-network capacitor C 1 in SM 1 and SM 2 , respectively. It can be seen that one SM's qZS-network capacitance varying is dominant on the dc-link voltage ripple of that SM, for instance, variations of C 11 have large effects on r vDC1 , but little effects on r vDC2 ; and r vDC2 is more largely affected when both C 11 and C 21 vary than only C 11 varies. In all cases, all the ripples are less than 1% even at the ±50% parameter variations.
In an case, the tolerance of commercial inductors is usually within ±20%, and that of commercial capacitors is within ±25%. Usually a margin is adopted when selecting the passive components in practice. Then, as long as the inductance and capacitance are within the tolerance, the effects caused by circuit parameters mismatch are very little on the proposed control.

V. CONCLUSION
This article proposed a duty-cycle predictive control method for dc grid integration of qZS-MCC PV power system. The discrete-time circuit models of grid-connected current, qZS-HB input current, and qZS-network capacitor voltage were derived. Based on that, the active-state duty cycles and shoot-through duty cycles of the qZS-MCC SMs were predicted for the modulator to achieve the global grid-connected current control and each SM's dc-link voltage balancing control. The controller design and implementation of the proposed method got much simplified, resulting into less design effort needed than the conventional methods, due to no need of compensator parameters or weighting factors in the predictive control loop. Comparison results showed good steadystate stability, fast dynamic responses, and high robustness of the system using proposed method, compared with the PI-based control. The potential limitation of the proposed method would be to employ a PI regulator in the MPPT control of each submodule. Future work will be conducted on eliminating the PI regulator, i.e., achieving full predictive control of the system.