Research Article  Open Access
Wenbao Hou, Guojun Tan, Delu Li, "An Improved MPCBased SVPWM Mechanism for NPC ThreeLevel ZSource Converters", Mathematical Problems in Engineering, vol. 2020, Article ID 4651823, 12 pages, 2020. https://doi.org/10.1155/2020/4651823
An Improved MPCBased SVPWM Mechanism for NPC ThreeLevel ZSource Converters
Abstract
Model predictive control (MPC) method has been widely used to reduce the computational complexity of the traditional space vector pulse width modulation (SVPWM). However, for a neutralpoint clamped threelevel Zsource converter, the performance of the normal MPC strategy would highly depend on the computation processing rate because of the multiple times optimization calculation. In this paper, an improved MPC strategy has been developed, with a voltage prediction being designed to replace the current prediction, the calculation of the roll optimization could be effectively simplified significantly, and then the digital execution efficiency would be improved. Besides, in order to obtain a fixed output harmonic frequency, a combination of this improved MPC and SVPWM has been studied and the shootthrough state insertion for the Zsource also has been analyzed in detail. Lastly, comparison experiments have been carried out to make verification of this improved modulation mechanism.
1. Introduction
NPC threelevel converters have significant advantages, e.g., smaller device pressure, lower , and better harmonic distortion in the output [1, 2]. With a Zsource network, this NPC threelevel converters would have a wide range of adjustable voltage, some allowed shootthrough states and better harmonic distortion in the output, and have been widely used in the photovoltaic(PV) gridconnecting system and the ac drive field [3–8]. For example, a switched quasiZsource DCDC inverter has been used for PV Systems [9], and a novel Zsource threelevel fourleg inverter has been researched to reduce the leakage current for threephase PV inverters [10]. Nevertheless, the control difficulty, e.g., modulation method and stability assurance, would also increase because of the existing of Zsource network.
In terms of modulation, many improved algorithms have been proposed, e.g., in [6], the space vectors pulse width modulation along with the shootthrough insertions were introduced to the single Zsource NPC threelevel inverters. A pulse width modulation (PWM) based on the stagespace averaging model was researched in [11] for a novel quasiZsource inverter topology. In [12], a new modulation strategy was studied in detail to reduce the leakage current for the Zsource fourleg inverters. In [13], a hybrid switching method with the combination of the PWM and pulse amplitude modulation (PAM) was proposed in details, which might result in a complicated computation and a high switching frequency and a switching loss reduction method based on a modified space vector modulation strategy [14].
In the past few years, the finite control set model predictive control (FCSMPC) has been widely used in the modern power electrical areas for its fast response and being suitable for the multivariable and nonlinear systems [1, 15, 16]. In [17], the high performance MPC method has been used for the quasiimpedance source inverter and a FCSMPC method was studied in [18]for the quasiZsource fourleg inverters with the consideration of an unbalanced load condition. In [19, 20], model predictive control based on the discrete models were also presented. In [21], the MPC strategy with a ripple power compensation structure was presented for the Zsource converters, and the corresponding output harmonic distortions were random which were unsuitable for the filtering.
Unfortunately, when the MPC method was used for the NPC threelevel converters, the control performance could be influenced because of the excessive optimization calculations, and for these NPC threelevel converters, which combined with the Zsource network, how to make insertions for the shootthrough states is also one of the difficulties. In [22], a modified MPC method by using a novel voltage prediction has been studied for the gridconnected Ttype inverter, which could improve the execution efficiency.
In order to solve the above problems and develop an efficient modulation approach for the NPC threelevel ZSC to simplify the control complexity, an improved MPCbased SVPWM mechanism has been presented in this paper. In detail, a voltage prediction was designed instead of the normal current prediction, and the calculation of the roll optimization could be simplified significantly although the optimization times are the same. Besides, in order to obtain a relative fixed output harmonic frequency, the optimized voltage vector resulted from the improved MPC method then was generated by the basic vectors of the normal SVPWM and the insertions of the shootthrough states also have been studied in detail.
This study is organized into five sections. Following the introduction, the operation principle of the NPC threelevel ZSC is explained in Section 2. In Section 3, this improved MPCbased SVPWM mechanism has been introduced in detail with the comparison to the traditional MPC method. Section 4 illustrates the experimental results with the performance comparisons between the traditional SVPWM strategy. Finally, some conclusions are drawn in Section 5.
2. Operation Principle of the NPC ThreeLevel ZSource Converters
The NPC threelevel ZSC researched in this paper is shown in Figure 1, containing two independent DCpower supplies. The connection point O of supplies is also regarded as the zero potential linking with the clamped point.
If the three up switches turn on (e.g., SA_{1}, SA_{2}, and SA_{3}), it is called upper shootthrough (UST) status being denoted as status “U.” On the contrary, if the three down switches turn on, it is called down shootthrough status (DST), which is represented as status “D.” The different states of this topology is summarized in Table 1.
 
Here, X = A, B, or C. 
Hypothesis C_{1} = C_{2} and L_{1} = L_{2} (means V_{C1} = V_{C2} = V_{C} and V_{L1} = V_{L2} = V_{L}). All the different states described in Table 1 can be summarized as three kinds of working conditions: nonshootthrough, UST, and DST. They are shown in Figures 2(a)–2(c), respectively. From Figure 2(a), several equations can be derived as follows:
(a)
(b)
(c)
Similarly, the equations derived from Figures 2(b) and 2(c) are as follows:
Here, the time duration of UST status is denoted as T_{sh_U} and T_{sh_D} for DST status. Normally, T_{sh_U} should be equal to T_{sh_D} in order to reduce the output voltage harmonic components, which means
At the steady state, the average voltages across L_{1} and L_{2} keep zero over the sampling period T_{S}, and the following equation could be derived from equations (1)–(3):where is defined as the duty ratio of the shootthrough states.
According to equations (1) and (6), for the nonshootthrough state, the output voltage V_{i} could be obtained as
For the Up or Down shootthrough states, the output voltage V_{i} could be obtained according to equations (2), (3), and (6):
Now, the three output voltages could also be represented as
And the output phase voltage U_{x} could be derived aswhere M is the modulation coefficient and H = 1/(12D) represents the booster ratio.
3. An Improved MPCBased SVPWM Mechanism
3.1. Traditional MPC
The mathematical model of the NPC threelevel ZSC in αβ coordinates can be given aswhere R and L are the load resistance and inductance, respectively.
By using the Euler approximation for a sampling time T_{s} (shown in equation (12)), equation (10) is discretized as in equation (13):where is the output current in coordinates, stands for the output voltage also in coordinates, which is determined by the 27 switching states of the NPC threelevel ZSC, and k is the kth sampling period.
From this mathematical model, the predictive output current at (k + 1)th could be derived as
For the traditional MPC strategy, a roll optimization of objective function could be set, as shown in equation (15), for the current trajectory control:where and are the given current components, respectively, and and are the predictive current components from equation (14).
Obviously, for this traditional method, 27 cycles of optimization should be conducted to obtain the smallest and the corresponding optimal switching state, in which equation (13) need to be also calculated 27 times in order to obtain the current components with different input voltages, which significantly increases the computation consumption. The implementation flow chart of the traditional MPC strategy is shown in Figure 3.
3.2. Improved MPC
For equation (14), the input voltage can be represented as
Assume that the predictive output current in equation (15) equals the given current components in ideal condition, which means
With the combination of equations (16) and (17), the predictive voltage components could be obtained aswhere superscript “p” means the expected value and is the reference current at (k + 1)th sampling, while the is the actual current at kth sampling.
For the improved MPC strategy, the roll optimization of objective function was set as
In order to make compensation of the time delay, equations (18) and (19) are shifted one step forward. Thus, the predictive voltage components and the objective function at (k + 1)th could be derived as equations (20) and (21):
The implementation flow chart of this improved MPC strategy then could be derived, as shown in Figure 4.
It is obvious that, for the improved MPC, the current calculation within the roll optimization has been omitted, which could improve the execution efficiency to a great degree.
On the other aspect, for the prediction accuracy, the predictive voltage error could be derived with equations (16) and (18):
From (22), it can be seen that the voltage tracking performance is consistent with the current, which provides the validation of the proposed improved MPC strategy.
3.3. Insertion of the ShootThrough States
For both the traditional and improved MPC strategies, their output frequency is a varying variable, which is unsuitable for the filtering design. Here, the optimized voltage u_{opt}(k) (the corresponding switch state is S_{opt}) has been implemented by the basic space voltage vectors and based on which the shootthrough states of the Zsource are inserted to ensure the boost performance. The MPCbased SVPWM mechanism is shown in Figure 5.
Shoottrough states’ insertion not only determines the boost performance but also affects the output harmonic distortion and the switch losses. For the space voltage vectors shown in Figure 6(a), it is being taken as an example that the obtained optimized voltage u_{opt} locates in Zone I and triangle 3, as shown in Figure 6(b).
(a)
(b)
Assume that the initial switch state is “0 −1 −1,” which means SA2, SA3, SB3, SB4, SC3, and SC4 are turned ON:(1)At t = t1, state “0 −1 −1” should be switched to “1 −1 −1” (for phase A, SA is changed from “0” to “1”), and the UST could be inserted in phase A by previously turning on the switch “SA1,” as shown in Figure 7 (SA1, SA2, and SA3 are ON while SA4 are OFF). During this insertion, the switch states for phases B and C remain unchanged, which satisfy the “voltsecond” principle.(2)At t = t2, state “1 −1 −1” should be switched to “1 0 −1” (for phase B, SB is changed from “−1” to “0”). If the UST is previously inserted in phase B, the switch state of phase A could be kept as “1,” while the switch state of phase C should be clamped from “−1” to “0,” which means the “voltsecond” state would be destroyed so this insertion should be omitted.(3)At t = t3, state “1 0−1” should be switched to “1 0 0” (for phase C, SC is changed from “−1” to “0”). The DST could be inserted in phase C by persistently turning on the switch “SC4,” as shown in Figure 7 (SC2, SC3, and SC4 are ON while SC1 are OFF). During this insertion, the switch states for phases A and B remain unchanged, which satisfy the “voltsecond” principle.
Obviously, when the reference vector is located in Zone I and triangle 3, the UST and DST can be inserted in the interaction range of the equivalent zero vector. Thus, the condition of T_{sh_U} = T_{sh_D} can ensure the balance of the UST status and the DST status.
From Figure 7, it could be easily seen that both the up and down shootthrough states would increase the output voltage (comparing Ref.Va(SA’) and Ref.Va(SA) and Ref.Vc(SC’) and Ref.Vc(SC)).
4. Experimental Results
In this paper, the effectiveness of the proposed improved MPCbased SVPWM mechanism is verified via an established experimental platform, as shown in Figure 8, along with the deep comparisons with the traditional SVPWM method. The detailed parameters are listed in Table 2. The control algorithm is implemented on a TMS320F28335 DSP with floatingpoint arithmetic.

Firstly, when the input voltage V_{dc} changes from 100 V to 200 V (V_{dc1} = V_{dc2} change from 50 V to 100 V), the corresponding dynamical line and phase voltages of the improved strategy are shown in Figure 9.
(a)
(b)
However, because of the voltage prediction error shown in Figure 10, there is some voltage ripple existing in the DClink voltage.
When the duty ratio D changes from 0 to 0.3, which means the output voltage of the Zsource topology V_{i} could be 2.5 times as much as the input voltage V_{dc} (according to equation (7)), the dynamical output line and phase voltages u_{ab} and u_{a} from the traditional SVPWM method and the improved proposed MPCbased SVPWM mechanism are shown in Figures 11 and 12, respectively.
(a)
(b)
(a)
(b)
Correspondingly, the output voltage V_{i} and the capacitors’ voltages V_{c1} and V_{c2} are shown in Figures 13 and 14. It is obvious that V_{i} changes from 100 V to about 250 V and the capacitors’ voltages are basically guaranteed to be in equilibrium.
For the output current, the dynamic comparisons are shown in Figures 15 and 16 along with the harmonic distortion analysis by taking aphase current as an example.
(a)
(b)
(c)
(a)
(b)
(c)
From Figures 15 and 16, it can be seen that the harmonic distortion changes from 3.69% to 2.11% for the traditional and improved methods without the booster function (D = 0), while from 4.20% to 3.53% with the insertion of the shootthrough states (D = 0.3), which could make verification of the improved mechanism studied in this paper. Besides, with the improved MPCbased SVPWM mechanism, the harmonic frequency is a relative fixed value, which is suitable for the filter designing. Besides, after the dynamic change, the restability time is about half an cycle for this improved MPCbased SVPWM, which is faster than the traditional SVPWM method (about one cycle).
In order to exhibit the superior property of the improved MPCbased SVPWM mechanism. The execution time comparisons between the proposed method, the traditional SVPWM, and the normal MPCbased SVPWM are summarized in Table 3, where the execution time is calculated by averaging tentime measured results when D = 0 and D = 0.3 and the sampling frequency is 10 kHz.

For the normal MPCbased SVPWM method, it has 10.03% and 13.91% time savings than the traditional SVPWM for the complicated trigonometric calculations has been omitted. Similarly, for the calculation reduction in the roll optimization, the improved scheme has over 26.25% and 19.25% time saving improvements than the traditional SVPWM and the normal MPCbased SVPWM when D = 0, while 28.78% and 17.27% when D = 0.3.
5. Conclusions
In this paper an improved MPCbased SVPWM mechanism has been proposed for the NPC threelevel ZSC. Firstly, in order to improve the execution efficiency, a novel voltage prediction has been derived based on the mathematical models to replace the normal current prediction, by which the optimization could be effectively simplified along with a relative nice performance. Besides, with the combination of the improved MPC and SVPWM, the harmonic frequency of the output current could be kept relatively fixed to be suitable for the filtering design and the shootthrough states insertions have been also studied to realize the voltage boosting. Lastly, comparison experiments have been carried out to make verification of this improved MPCbased SVPWM mechanism. In particular, this improved method has a similar static performance to the traditional SVPWM with a better dynamic performance, while for the execution efficiency, it has over 26.25% and 19.25% time saving improvements than the traditional SVPWM and the normal MPCbased SVPWM when D = 0, while 28.78% and 17.27% when D = 0.3, which is suitable for the digital implementation.
Data Availability
The processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by Research Foundation of JiangSu Collaborative Innovation Center for Building Energy Saving and Construction Technology (no. SJXTBS1704); Jiangsu University Natural Science Research Project (No. 18KJB470024).
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Copyright © 2020 Wenbao Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.