Design and Control of a Quasi-Z Source Multilevel Inverter Using a New Reaching Law-Based Sliding Mode Control

: The rapid growth in renewable energies has given rise to their integration into the grid system. These renewable and clean energy sources are dependent on external conditions such as wind speed, solar irradiation, and temperature. For a stable connection between these sources and power grid systems, a controller is necessary to regulate the system’s closed-loop dynamic behavior. A sliding mode control (SMC) using a new reaching law is proposed for the integration of a Modiﬁed Capacitor-Assisted Extended Boost (MCAEB) quasi-Z Source 7 level 18 switch inverter with the grid. An SMC-based controller was implemented to regulate the current ﬂow between the inverter and the grid. SMC has the advantages of ease of implementation, robustness, and invariance to disturbance. The simulation results of SMC and the proportional integral (PI) controller are compared in terms of settling time, steady-state error, and total harmonic distortion (THD) during transient response, steady-state response and step response under different operating conditions. A hardware-in-loop (HIL)-based experimental setup of MCAEB quasi-Z source multilevel inverter was implemented using OPAL-RT. The performance of the proposed controller was further validated by implementing it on DSPACE-1202.


Introduction
The increased demand in electrical energy has resulted in greater consumption of fossil fuels. To fulfil the demands of future generations without adversely affecting the climate, renewable energies such as wind, solar, tidal, nuclear and hydroelectric power need to be integrated into power grid systems. Unfortunately, most renewable energies are highly intermittent in nature, and are dependent upon external conditions such as wind speed, temperature, weather, humidity, etc. [1]. Researchers have suggested ways of mitigating these problems, in order to design a sustained and resilient energy system that is able to operate under various environmental conditions [2][3][4]. To counter this issue, the electricity generated from renewable sources is converted to DC and then to AC in order to provide non-varying frequency and voltage.
Inverters are essential components for the integration of variable clean energy sources into power grid systems at grid frequency and voltage. Multilevel inverters (MLI) are preferred because of their clean sinusoidal voltage waveform, increased power quality, and their minimization of total harmonic distortions (THD), which reduce the requirements of A suitable controller is needed for the stable connection of distributed energy resources (DER) with the grid. Active and reactive power control, grid synchronization, and DC link voltage control, are important parameters that need to be controlled by the gridside controller. Liu et al. [24] classified controllers based on number of feedback loops as single loop, double loop and triple loop. Cascaded control was used to achieve high performance. Athari et al. [25] provided a comprehensive review of controller classification based upon the nature of the controller. Sliding mode control (SMC) is preferred for its convenient implementation, and invariance when encountering external disturbances and uncertainties. For these reasons, SMC has been applied in various fields of study; for example, Piao et al. [26] demonstrated the implementation of sliding mode control in positioning systems for unmanned vessels, and Xu and Ran [27] implemented a sliding mode control in a simple qZSI three-phase inverter. Classical SMC has the disadvantages of chattering and a slow convergence rate, which were addressed by Xiu and Guo, who designed a novel reaching law [28]. SMC-based control using this novel reaching law is proposed for an MCAEB qZSI-based grid-tied multilevel inverter in this paper. The novel reaching law consists of two parts, which affect the convergence rate depending upon whether the system is near or far from the sliding surface. The major contributions of this paper are as follows: • Analytical model of MCAEB qZSI is derived and simulated in MATLAB/Simulink. An SMC-based current controller is derived for the regulation of grid injected current. A control law is derived using a linear sliding mode-based surface and a novel reaching law to achieve faster convergence rate. The controller achieves robust behavior, fast response, and lower output current ripples under a variety of operating conditions. • This paper proposes a fast-acting SVPWM in the gh frame of reference for the modulation of MCAEB qZSI multilevel inverters. The transformation of the reference signal from the dq to the gh frame of reference simplifies the calculation of the switching ratio between different inverter switching states. Its simple implementation and fast computational ability have an inherent advantage over traditional SVPWM techniques.

•
The performance evaluation of the sliding mode control with a new reaching law under different operating conditions is investigated in terms of different parameters such as settling time, steady-state error, and THD. The results are then compared with classical controllers such as the proportional integrator (PI) controller in order to determine the effectiveness of the proposed controller for the proposed inverter.

Model of MCAEB Quasi-Z Source Network
The circuit configuration of MCAEB qZSI is shown in Figure 1. The qZSI consists of three inductors L 1 , L 2 and L 3 , four capacitors, C 1 , C 2 , C 3 and C 4 and two diodes, D 1 and D 2 . Three such qZSI are connected in series to create DC link voltage. The output DC link voltage is then connected to a 7-level 18-switch multilevel inverter as shown in Figure 1. The inverter is connected to the grid via LCL filter. V 1 , V 2 and V 3 are the input DC voltage source. I L1 , I L2 and I L3 are the currents through L 1 , L 2 and L 3 respectively. Similarly, V c1 , V c2 , V c3 and V c4 are the voltages across C 1 , C 2 , C 3 and C 4 respectively. i 1,abc , i 2,abc are the currents through the two filter legs as shown in Figure 1, while v c,abc is the voltage across the capacitor in the filter. A symmetric system qZSI is assumed, such  The operation of qZSI is divided into two states, the Shoot-Through (ST) and Non-Shoot-Through (NST) states, respectively as shown in Figure 2. The equivalent circuits of these two states of the qZSI are shown in Figure 2. During NST, the inverter operates under normal modulation. Meanwhile, the ST state is achieved by shorting any two complementary switches simultaneously in the inverter, such as and , where = 1 9.  The operation of qZSI is divided into two states, the Shoot-Through (ST) and Non-Shoot-Through (NST) states, respectively as shown in Figure 2. The equivalent circuits of these two states of the qZSI are shown in Figure 2. During NST, the inverter operates under normal modulation. Meanwhile, the ST state is achieved by shorting any two complementary switches simultaneously in the inverter, such as S an and S an , where n = 1 to 9. The operation of qZSI is divided into two states, the Shoot-Through (ST) and Non-Shoot-Through (NST) states, respectively as shown in Figure 2. The equivalent circuits of these two states of the qZSI are shown in Figure 2. During NST, the inverter operates under normal modulation. Meanwhile, the ST state is achieved by shorting any two complementary switches simultaneously in the inverter, such as and , where = 1 9.     Figure 2a presents the equivalent circuit of MCAEB qZSI. Current source represents the inverter. A representation of the state space during Active State is as follows. where i L0 is the current input to the inverter and Z o represents the equivalent load across the inverter. This current is directly proportional to the switching state and output load current injected to the grid.

ST State
By switching on any two complementary switches, e.g., S an and S an where n = 1 to 9, this state is achieved. In this state, the diodes in the qZSI become reverse biased and turn off because of capacitor voltages. Figure 2b shows the equivalent circuit of qZSI in the NST state. The state space of the NST state of MCAEB qZSI can be represented as follows. .
Then, the dynamic mathematical model of the qZSI is given by This D signal can be obtained by comparing the duty ratio with the carrier wave, which can be then be applied to inverter modulation to achieve switching pulses such that the terminals across qZSI network are shorted.

Modulation
The switching of the inverter is achieved through Space Vector Modulation (SV-PWM). A new frame of reference, i.e., gh, is introduced in which the g and h axes are 60 • apart. By using this transformation, the duty ratio and appropriate switching state of the inverter can be easily selected through comparison, which can be implemented with the use of simple if/else conditions. This improves the efficiency, readability, and fast application of SVPWM. Figure 3a shows the vector representation of the transformation. The transformation can be written as shown below [23]: where Energies 2022, 15, x FOR PEER REVIEW 6 of 18 where and are the distance between ⃗ and ⃗ , and ⃗ and ⃗ , respectively as shown in Figure 3. By rearranging Equation (8), we get: For phase voltages, k = 1 is used. θ r is the coordinate reference angle, and n is the number of positive voltage levels. By using this transformation, we obtain mg and mh values based on the current location of reference vector. The → ρ 1 and → ρ 2 can be easily projected from the reference vector → V r , as shown in Figure 3b. Therefore, → V r can be written as follows: where l 1 and l 2 are the distance between → V 1 and → V 3 , and → V 2 and → V 3 , respectively as shown in Figure 3. By rearranging Equation (8), we get: From this, the duty cycle can be deduced as where d 1 , d 2 and d 3 are the duty cycle ratio for vectors To achieve → V r at the output of the inverter, these vectors need to occur in these percentages of the total time period T s . For a balanced power system, the distance l 1 and l 2 are assumed to be equal, i.e., l 1 = l 2 = 1. This simplifies the calculation for determining the duty ratio compared to conventional means, which require the calculation of the inverse of a matrix during runtime, and are thus very quick and efficient. Through appropriate selection of the switching state of the inverter corresponding to → V 1 , → V 2 and → V 3 , and using Equation (9), the switches are turned on in such a way that a sinusoidal three-phase voltage is achieved at the inverter output, using the switching strategy shown in Figure 4. Here, when the carrier wave is less than lower D/2, the system is in the ST state. When the carrier wave is greater than D/2 and less than d 1 , a switching state is applied so that the vector → V 1 is created at the output of the inverter. Similarly, when the carrier wave is greater than d 1 and less than d 2 , the vector → V 2 voltage is at the output of the inverter. When the carrier wave exceeds upper D/2, the system will again enter the ST state. This is done in such a manner that the NST states occur in the middle of the switching period rather than at one end of the switching period as shown in Figure 4.
A filter is an important part of any inverter, and helps to reduce the THD according to the IEEE standard for grid integration and smooth power delivery. The equivalent circuit of the LCL filter used is shown in Figure 5.
A Clarke's transformation is used to change the abc frame of reference of all state variables and parameters into an αβ frame of reference. v inv , v g , i 1 , i 2 and v c represent the voltage across the inverter output legs, grid voltage, current through inductors L f , current through L g , and voltage across the capacitors in the αβ frame of reference.  A filter is an important part of any inverter, and helps to reduce the THD according to the IEEE standard for grid integration and smooth power delivery. The equivalent circuit of the LCL filter used is shown in Figure 5. A Clarke's transformation is used to change the abc frame of reference of all state variables and parameters into an frame of reference. , , , and represent the voltage across the inverter output legs, grid voltage, current through inductors , current through , and voltage across the capacitors in the frame of reference.  A filter is an important part of any inverter, and helps to reduce the THD according to the IEEE standard for grid integration and smooth power delivery. The equivalent circuit of the LCL filter used is shown in Figure 5. A Clarke's transformation is used to change the abc frame of reference of all state variables and parameters into an frame of reference. , , , and represent the voltage across the inverter output legs, grid voltage, current through inductors , current through , and voltage across the capacitors in the frame of reference. Sliding mode control forces the system's state trajectories to move towards a sliding surface. Once the states arrive at the sliding surface, the states slide towards the equilibrium point. A sliding mode surface needs to be chosen. Then, a control law is designed such that states will be forced towards the sliding surface. The sliding mode surface in this article is defined as: σ is the sliding surface of our control system. i * 1 , i * 2 and v * c are the references which should be followed. c 1 , c 2 and c 3 are the sliding mode surface coefficients. Since, the state parameters in both the α and β axes are the same, therefore, c 1 , c 2 and c 3 will be the same for both axes. By differentiating Equation (12) and inserting values from Equation (11), we get By making . σ αβ = 0 in Equation (13), we can achieve the equivalent control law u eq for our controller. where A control input consists of an equivalent control law and a reaching law. A novel and improved reaching law, as proposed by Xiu and Guo [28], is used. The control law in this research work uses the new reaching law, which can be written as: where 0 < α < 1, k 1 > 0, k 2 > 0 and b = 1 + k 2 /k 1 . During reaching phase in this approach, when the system is far from the sliding surface, i.e., |σ| > 1, the first part of the equation speeds up the reaching rate of the system towards sliding mode surface. When the system approaches the sliding surface, i.e., |σ| < 1, the second term plays a vital role. For a Lyapunov function of L(t) = σ 2 /2 , the system is stable when the following condition is met: .
If and only if σ = 0 does the equality hold up. Therefore, the stability can be proved. Equation (19) holds up when the following conditions are met: To determine the stability of the system when disturbance d(t) is present in the system, Equation (11) is modified into Equation (23). Using this system, k 1 and k 2 need to be greater than |d(t)| for the system to be stable, as shown in Equation (24). .

DC-Side Control
The assumption is made that all qZSI present in the system behave identically, since the parameters are the same and a balanced load is connected. Based on Equation (18), the reference DC link voltage can be obtained. This DC voltage can then be used to calculate the reference voltage across the capacitor C 1 and C 2 of qZSI, obtained by using volt-sec balance across inductors and capacitors, as follows: where Z o is the equivalent impedance observed by the qZSI, which is used to determine the currents flowing through inductors L 1 and L 2 , respectively.
The sliding surface selected for the dc voltage control is given by Equation (28).
Selection of the sliding mode coefficients is important so that the system states move towards equilibrium. To achieve this convergence, the following control law is used, where t ST is the shoot-through time period while T s is the total switching time period.
3. Results Figure 6 shows the control schematic for the proposed topology. A simulation analysis for the proposed controller for a grid-tied inverter was carried out under a variety of operating conditions using the design parameters shown in Table 1. The operating conditions are described below. Figure 6 shows the control schematic for the proposed topology. A simulation analysis for the proposed controller for a grid-tied inverter was carried out under a variety of operating conditions using the design parameters shown in Table 1. The operating conditions are described below.      Figure 7 shows the response of MCAEB qZSI using the SMC-based controller under different operating conditions. Figure 7a,b show the output current under normal voltage conditions (NGO), with the step of the reference input current set at 0.15 s. By analyzing the output current response using the SMC controller, it can be observed that the rise time, percentage overshoot, settling time and THD are equal to 2.361 ms, 8.152%, 11.405 ms and 1.08%, respectively, under NGO.   Figure  7d. An increase in THD from 1.08% to 3.59% can be observed, which is below the 5% regulation under IEEE-63547. The current response during grid voltage sag and swell are shown in Figure 7e,f, respectively. Under these conditions, there is almost no change in output current when voltage sag or swell occurs at 0.1 s. This shows the robustness of the proposed controller to external disturbances.

Results
Similarly, Figure 8 shows the DC link voltage under different operating conditions.   Figure 7c shows the output current I 2 during AGO, and the THD is shown in Figure 7d. An increase in THD from 1.08% to 3.59% can be observed, which is below the 5% regulation under IEEE-63547. The current response during grid voltage sag and swell are shown in Figure 7e,f, respectively. Under these conditions, there is almost no change in output current when voltage sag or swell occurs at 0.1 s. This shows the robustness of the proposed controller to external disturbances.
Similarly, Figure 8 shows the DC link voltage under different operating conditions.  Figure 7e,f, respectively. Under these conditions, there is almost no change in output current when voltage sag or swell occurs at 0.1 s. This shows the robustness of the proposed controller to external disturbances.
Similarly, Figure 8 shows the DC link voltage under different operating conditions. Figure 8a-d show the DC link voltage during NGO, AGO, and voltage sag and swell in grid voltage, respectively. A rise time of 432.45 µs, 38.067% overshoot, settling time of 13.12 ms and a steady-state error of almost 1 V can be observed. The output current of the inverter using the PI-based controller is shown in Figure 9. By analyzing these responses, it can be observed that the controller has a rise time of 4.314 ms, 29.5% overshoot, a settling time of 35-40 ms, and a THD of 1.87% and 22.88% during NGO and AGO, respectively. A slight change in output current can be observed during voltage sag and swell in grid voltages. It can be seen that the SMC controller performs better than the PI controller when disturbance in grid voltage is applied.
Similarly, the DC link voltage is shown in Figure 10 under different operating conditions, with a rise time, percentage overshoot, settling time and steady-state error of 1.632 ms, 128%, 50 ms and 1 V, respectively. Additionally, the link voltages are shown for voltage sag and swell in grid voltage in Figure 10c,d, respectively. This shows that the SMC controller for DC side performs better than the PI controller, as it has a lower rise time, overshoot percentage and settling time. The output current of the inverter using the PI-based controller is shown in Figure 9. By analyzing these responses, it can be observed that the controller has a rise time of 4.314 ms, 29.5% overshoot, a settling time of 35-40 ms, and a THD of 1.87% and 22.88% during NGO and AGO, respectively. A slight change in output current can be observed during voltage sag and swell in grid voltages. It can be seen that the SMC controller performs better than the PI controller when disturbance in grid voltage is applied.  Similarly, the DC link voltage is shown in Figure 10 under different operating conditions, with a rise time, percentage overshoot, settling time and steady-state error of 1.632 ms, 128%, 50 ms and 1 V, respectively. Additionally, the link voltages are shown for voltage sag and swell in grid voltage in Figure 10c,d, respectively. This shows that the SMC controller for DC side performs better than the PI controller, as it has a lower rise time, overshoot percentage and settling time.

Experimental Results and Discussion
An HIL setup is established for the experimental verification of the proposed controller for the grid-tied inverter. The experimental setup consists of an OPAL-RT-based PXIe-1085 real-time power grid simulator, an NI PXIe-6738 DAQ card, an SCB-68a I/O connector, an RTA-4004 Oscilloscope and a DSPACE-1202-based Microlab-box, as shown in Figure 11. The proposed topology is simulated in real time using OPAL-RT. The SMC controller is deployed on the DSPACE-1202 using the DSPACE control Desk application. A DAQ card along with an I/O connector is used to create a feedback loop with the DSPACE.  Figure 12a. Similarly, the three-phase output current during operation of the open loop system is shown in Figure 12b. Figure  13-15 show the current response of the inverter when the SMC-based closed loop controller is applied on dspace-1202 with a time step of 100µs.   Figure 12a. Similarly, the three-phase output current during operation of the open loop system is shown in Figure 12b. Figure  13-15 show the current response of the inverter when the SMC-based closed loop controller is applied on dspace-1202 with a time step of 100µs.    Figure 15a shows the step response of single-phase current from 20 A to 40 A,  Figure 15a shows the step response of single-phase current from 20 A to 40 A, while Figure 15b shows the three-phase output current obtained from the RTA-4004 oscilloscope.   Figures 13 and 14 show the output current when reference currents of 20 A and 40 A are applied, respectively. These results show that the controller follows the reference current. Figure 15a shows the step response of single-phase current from 20 A to 40 A,   Figure 15a shows the step response of single-phase current from 20 A to 40 A, while Figure 15b shows the three-phase output current obtained from the RTA-4004 oscilloscope.

Conclusions
This paper proposes a single-stage sliding mode control using an advanced reaching law to provide both DC link voltage and inverter control for a high-switching-frequency modified capacitor-assisted extended boost quasi-Z source multilevel inverter. An optimized topology for a multilevel three-phase inverter was selected to achieve a trade-off between switching loss and the higher number of levels. To achieve fast control, dq-gh transformation-based SVPWM was used because of its fast action, which is required at higher switching frequencies. A comparison was performed between the proposed control strategy and a PI controller on the basis of a simulation. The results of the simulation showed that the proposed controller demonstrated an extraordinary performance compared to PI-based controllers under normal and harmonic-infested grid connections. It showed strong robustness, invariance to disturbance, fast response, higher-quality current, and lower THD. Hardware-in-loop implementation was performed in Smart Grid Laboratory, and the experimental results were in agreement with the simulations, thus validating the feasibility and effectiveness of the control.