Design and Development of Fixed-Frequency Double-Integral SM-Controlled Solar-Integrated Bidirectional Quasi Z-Source DC-DC Converter in Standalone Battery Connected System

DC microgrids have been quite popular in recent times. *e operational challenges like control and energy management of the renewable-driven standalone DC microgrids have been an interest of research. *is paper presents a bidirectional quasi Zsource DC-DC converter (BQZSDC). *is converter topology has been developed based on a conventional buck-boost type bidirectional converter, and it interfaces the storage system and the common DC bus. *e challenge, however, lies in effectively managing the uncertain renewable energy sources and the storage system and catering for the loads simultaneously. An effective control strategy is needed for that energy management and to achieve various microgrid objectives. *is paper deals with one such effective control strategy implemented for BQZSDC. *at is, the fixed-frequency double-integral sliding mode control (FF-DISMC) controls the converter to regulate the DC bus voltage and battery current. A detailed analysis of the controller is conducted, and its performance is evaluated for both charging (buck) and discharging (boost) modes. Simulations have been performed in MATLAB, showing that the controller performs satisfactorily in achieving the objectives of voltage regulation and battery current regulation. Finally, the performance of the proposed controller is validated with the hardware setup.


Introduction
Often, in applications requiring increased voltage, a conventional boost converter is a common choice. However, it is understood that voltage boosting is limited by duty cycle constraints because of the switching device performance and conduction loss [1][2][3]. erefore, topologies with higher voltage gain have been of great research interest. In this line, the Z-source network's novel and effective topology came into the limelight [4]. e initial implementation of this topology was limited to DC-AC application, where the topology was popularly known as Z-source inverter (ZSI). is converter also supports bidirectional operation with both buck and boost modes. A significant amount of literature has been devoted to the ZSI and its applications, such as interfacing renewable sources like PV wind [5][6][7]. An improved version of the inverter named quasi Z-Source inverter (QZSI), with added advantages of input current continuity and reduced voltage stresses of capacitors, was introduced [8].
For DC-DC applications, the concepts of Z-source converter and quasi Z-source converter (QZSC) are often used [9][10][11]. In [12], QZSC has been used in bidirectional power flow applications, where the buck and boost modes were individually controlled [13,14]. However, in the case of the converter connected to a standalone microgrid, it is essential that the DC link voltage is regulated in both modes of operation based on the power demand [14][15][16][17].
e Z-source and quasi-Z-source converters have simple architectures, and they can provide a significant gain [12]. e switched-inductor DC-DC converter proposed in [18] has high gain and low voltage stress, but it has more inductors. Reference [19] proposes a switched-capacitor-based Z-source DC-DC converter. In this topology, despite increased voltage gain, there is no common ground between input and output and it has high voltage stress across the switches.
e switched-capacitor quasi Z-source DC-DC converter proposed in [20] has high efficiency, but more switches are required. e bidirectional quasi Z-source converter proposed in [21] can provide high gain but does not have common ground.
is produces a du/dt issue between input and output. e proposed BQZSDC can provide high voltage gain. Its design is based on the bidirectional quasi Z-source DC-DC two-level converter. e main difference is changing the primary power switch to a different position. is BQZSDC has minimal voltage stress on power switches. Consequently, the BQZSDC can choose power switches with low rated voltage and low on-state resistance, which causes improvement in efficiency. At the same time, when compared with basic quasi Z-source, its gain has been decreased slightly, but it still meets the requirements of connection with different sources. e presence of common ground also avoids the du/dt issue. e conventional proportional-integral (PI) and dualloop PI-control techniques are commonly designed by linearizing the model at a particular operating point [22,23]. For higher-order systems, deriving a linearized model is complex. A reduced-order small-signal closed-loop transfer function model was presented in [24]. In this paper, traditional model order reduction procedures are utilized, and the inaccuracy of input-output mappings between the original and reduced-order systems is considerable. Wang et al. [25] propose to give a preprocessing strategy for realtime modeling of large-scale converters with inhomogeneous initial conditions to address input-output mapping problems. However, the transient behavior of these systems with linear controllers is poor under large-signal perturbations. is is because of the variaiton in small-signal models at different dc operting points. Several nonlinear controllers are utilized for power electronic converters to solve the above problems.
Sliding mode control (SMC) is a robust control approach that effectively handles parameter changes, external disturbances, and input disturbances. e hysteresis modulating sliding mode control (HM-SMC) technique used in [26][27][28] suffers from chattering and switching frequency variation under load fluctuations. In variable frequency operation, stabilizing the feedback control circuit could be difficult. Later, fixed-frequency SMC was developed using pulse width modulation [29], maintaining the constant frequency despite input voltage and load variations. is fixed-frequency SMC was based on an equivalent control switching function to harvest a trajectory near equivalent to an ideal sliding mode trajectory. SMC in conjunction with PWM reduces steady-state error (SSE) significantly. Integral SMC, which incorporates an integral term of the state variables into the SM controller, can further minimize SSE. A second integral component of the tracking error has been considered to improve the system's steady-state accuracy even more. Double-integral sliding mode controller (DISMC) responds quickly for a broader range of operating circumstances while significantly reducing SSE [30]. e model predictive control (MPC) computes the switch input from the converter's active model and provides a resolution for trajectory optimization [31]. e optimization techniques in MPC necessitate many computations, and MPC is not appropriately aimed at converters with large values of switching frequencies. References [32,33] proposed voltage source inverters based on adaptive error correction, with the error approach included in both the outer and inner prediction loops and a nonlinear state-space function to describe the AC microgrid along with an event-triggered consensus control technique. However, MPC requires a powerful processor to perform real-time calculations, but DISMC has very simple calculations. e advantage of the proposed FF-DISMC is its ability to reject disturbances and deal with system uncertainties better than MPC. e advantages of the proposed fixed-frequency doubleintegral SMC are as follows: (1) Fast dynamic responses compared with conventional voltage and current mode controllers (2) Characteristic robust features of SMC, but working at a fixed frequency (3) Stability over a wider range of operating conditions (4) e slight variation of the settling time over an extensive range of operating conditions (5) Stabilizing the feedback control circuit can be more difficult in variable frequency operation than fixedfrequency control e key contribution of this paper is the design and implementation of an FF-DISMC for the BQZSDC. e controller scheme was designed to regulate the DC grid voltage against variations in reference voltage and load power with bidirectional power flow. Figure 1 depicts the proposed system's architecture. e suggested converter simultaneously manages the PV system's power, battery, and load. When solar radiation is available, a maximum power point tracking (MPPT) algorithm ensures that the PV panel generates the most power possible. e suggested controller directs the battery to absorb excess energy from the PV panel or supply the load with the power it requires. Section 2 presents the system design and steady-state mathematical model of BQZSDC. e control strategy of FF-DISMC is analyzed in Section 3. e simulation and hardware results are shown in Section 4, comparison analysis in Section 5, and conclusions in Section 6.

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International Transactions on Electrical Energy Systems

System Design and Modeling
e following assumptions are made in the proposed BQZSDC to simplify the analysis: (1) e power switches' on-state resistance and the equivalent series resistance of the inductors L 1 , L 2 and capacitors C 1 , C 0 are Ignored. e ESR, r of capacitor C 2 , is considered to avoid complications in obtaining the state equations of the converter.
(2) e currents and voltages of the inductors and capacitors increase and decrease linearly. e topology of the BQZSDC is displayed in Figure 2, interfacing the battery storage to the load and DC bus. e topology primarily consists of three active switches, S 1 , S 2 , and S 3 . e converter has the bidirectional capability to charge/discharge the battery by adequately choosing the switching signals. In this paper, the operation of the converter in boost mode (discharging mode) is only analyzed; however, buck mode can also be operated similarly. In the boost mode of the converter, the switch S 1 acts as the main switch, whereas S 2 and S 3 are complementary switches to S 1 . e battery voltage V b is assumed to be constant. It is considered that BQZSDC is being operated in CCM, with switching input u and a constant switching frequency f. e converter operation can best be analyzed by observing the following two modes individually.
2.1. Mode 1: S 1 Is Turned On; S 2 and S 3 Are Turned Off (0 < t ≤ DT). In mode 1, S 1 is made on and switches S 2 and S 3 are made off. Once the switching status of the switches S 1 , S 2 , and S 3 is declared, the topology can be seen in Figure 3. On analyzing the circuit, it can be understood that the energy from the battery is stored in the inductor L 1 with S 1 being turned on. e capacitor C 2 gets energized through L 2 and C 1 (already charged). e load power in this mode is supplied by the output capacitor C 0 because the load is straight away not attached to the battery. e switching states in this mode are as follows: 2.2. Mode 2: S 1 Is Turned Off; S 2 and S 3 Are Turned On (DT < t ≤ T). In mode 2, S 1 is turned off and switches S 2 and S 3 are turned on. e topology can be seen as the equivalent circuit in Figure 4. As a consequence of the previous mode, the energy kept in the inductor L 1 charges the capacitor C 1 through S 2 . e energy kept in the inductor L 2 is used to feed the load R 0 , and the capacitor C 2 is discharged simultaneously. e switching states in this mode are as follows:    (10), we derive the system modeled as follows:

International Transactions on Electrical Energy Systems
where u indicates the switching state of S 1 and matrices A and B are as follows: e state vector includes five parameters: inductor currents i L1 and i L2 and capacitor voltages v C1 , v C2 , and v 0 . e state vector is presented as follows:

Fixed-Frequency Double-Integral Sliding
Mode Control e proposed FF-DISMC has two significant features. is controller is based on reduced state measures operating at a fixed frequency [29]. e advantage of fixed frequency operation is explained in Section 1. e output voltage measured and the remaining state variables are estimated to sense the minimum number of state variables. Here, the controller variables are errors in output voltage (v 0 ) and input current (i L1 ). e reference current (i ref ) for inductor L 1 is generated using voltage error: 3.1. Sliding Surface. e proposed FF-DISM control employs the output voltage (v 0 ) and battery side inductor current (i L1 ) errors as control state variables. Correspondingly, two more control state variables are added to the sum of the first two state variables as integrals and double integrals. e control variables are further shown as follows: For the control of BQZSDC, the switch input u should limit values between 0 and 1.
is control logic is developed by expressing the logic state of S 1 . e switching function is as follows: e FF-DISM controller's sliding surfaces are most likely to be interpreted as a linear combination of four state variables, which can be expressed as follows: where α 1 , α 2 , α 3 , and α 4 are the sliding coefficients.

Equivalent
Control. e dynamic model of the BQZSDC can be obtained by substituting a set of equations in (11) into the time derivative converter variables given in (15)- (18).
e derived equations are shown as follows: e equivalent control equation was derived by implementing equation _ s � 0.
International Transactions on Electrical Energy Systems 5 is gives the following: 3.3. e Architecture of the Proposed Controller. A PWM block and a group of control rules, which were based on indirect SM control, are used to implement the proposed FF-DISM controller [34,35]. e equivalent controller consists of a control signal v C and a ramp signal v ramp as follows: where e BQZSDC and the FF-DISM controller are shown in Figure 5. e control law includes the comparison of the two signals v C and v ramp . e ramp signal maintains the constant frequency.
For successful sliding mode operation, it is essential to satisfy three conditions. ese conditions are hitting conditions, existing conditions, and stability conditions. e hitting condition confirms that the state trajectory hits the sliding surface, which was guaranteed by the switching function used in (20).

Existence Conditions.
To examine the existence condition, it must satisfy the local reachability conditions given as follows: Replacing the derivative of (21) in (26), we can state the equation as follows: For BQZSDC, the existence conditions for the sliding mode operation are as follows: In the case-1, (27), we have the following: In the case-2, (28), we have the following: e values of battery voltage V b and output voltage V 0 are assumed within a limit, which typically depict an operating range of the converter. e existing condition at maximum and minimum values is sufficient to ensure the broad range of abidance. While designing a sliding mode controller, the existing conditions should be met for steadystate operation. At steady-state condition, the state variables v C1 , v C2 in (29), (30) are replaced by steady-state values V C1 (SS), V C2 (SS).
Equations (31) and (32) can show the resulting existing condition considering all presumptions: 3.5. Stability Condition. e stability condition for the controller was proved by first determining the system's ideal sliding dynamics and then analyzing its equilibrium point.

Ideal Sliding Dynamics.
By substituting u by u eq in (11), the large-signal discontinuous system model of BQZSDC gets converted into an SM continuous system and is given as follows: 6 International Transactions on Electrical Energy Systems en, substituting the equivalent control signal (23) in (33) gives the following: International Transactions on Electrical Energy Systems 7

Equilibrium-Point Analysis.
Consider that the ideal sliding dynamics finally settle at a stable equilibrium point on the sliding surface. If there is no input or loading disturbance, the system's dynamics will remain unchanged at this equilibrium point (steady state); i.e., the steady-state values at that operating point are given as follows: 8 International Transactions on Electrical Energy Systems

Linearization of Ideal Sliding
Dynamic. e ideal SM continuous BQZSDC system's small-signal state model was developed at stable equilibrium operating point (35).
International Transactions on Electrical Energy Systems e above equations are derived by assuming the validity of the following conditions: By rearranging the above equations in standard form, we get the following: e characteristic equation of the linearized system is given by the following: where International Transactions on Electrical Energy Systems e stability of the system is found by substituting (40) in (41). is, coupled with the existing condition (31) and (32), constitutes the foundation for selecting and designing the controller's control gains in conjunction with the converter's specified requirements.

Selection of Control Gains.
e sliding coefficients were chosen after analyzing the effect of changing the control gains on the output voltage. e subsequent conclusions were attained: (1) e increase in K minimizes the steady-state error but increases the settling time by making the transient response more oscillatory (2) e slope of voltage responses can be increased or decreased by changing k 1 (3) e increment in k 2 reduces the settling time but raises the steady-state error (4) e increment in k 3 reduces transient response overshoot while slightly increasing settling time e values of k 1 , k 2 , and k 3 are selected based on the above observations until the controller provides the required performance.

Results and Discussion
e proposed control technique was developed in MAT-LAB/Simulink and tested on a prototype. ese details are addressed in the subsections that follow.

Simulation Results.
e efficiency and performance of the proposed controller for the converter are examined based on a set of simulations. Even though the controller was developed using the boost mode approach, it can also be used in buck mode. is section analyzes the converter's responses for reference and load changes in both buck and boost modes.

Reference Change.
e effect of changing the reference voltage on the controller and its tracking ability is analyzed. e reference voltage was varied from 48 V to 36 V at 0.2 sec, and it is observed that the v 0 is tracking the new reference of 36 V, as shown in Figure 6. Furthermore, it can be seen that at 0.4 sec, the voltage is restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V. e parameters of the converter are mentioned in Table 1.
e converter can operate in step-up and step-down modes, thereby enabling the battery to charge or discharge depending on the power flow. e system was connected to a PV source interface with a load attached to the common bus. e load is desired to be catered for at a constant voltage of 48 V. If the PV power is more than the load power, the BQZSDC is switched to buck mode, and the excess energy is used to charge the battery. If the PV power is less than the load power required, the BQZSDC goes into boost mode, and the battery is discharged to make up the difference.
As a part of this work, a 12 V battery is considered, and the output reference voltage is taken as 48 V. e PV system acts as a constant source (operating at constant irradiation) current of 4.17 A supplying 200 W, connected at the load side of the BQZDC. e converter performance was observed under load variations.

Boost Mode (Discharging Mode).
In this mode, the battery starts discharging through the converter supplying the deficit power to maintain the power balance and a stable output voltage. As shown in Figure 7, the initial load demand is 5.2 A, out of which the PV source is supplying 4.17 A. e converter provides the remaining current of 1.03 A (stepping down the battery current from 4.16 A) and maintains the load voltage at 48 V. e load current was observed to be enhanced to 6.25 A at time t � 0.2 sec. e results show that the excess current of 2.08 A was supplied by the converter (stepping down the battery current from 8.33 A). Moreover, at t � 0.4 sec, the load current returns to 5.2 A, and the converter supplies excess current even under this condition. Figure 8 shows the variation of SOC of battery and load voltage.

Buck Mode (Charging Mode).
In this mode, the battery starts charging through the converter absorbing the excess power to maintain the power balance and a stable output voltage. Initially, the load current was 4.17 A which was exactly catered for by the PV. us, the battery remains idle with no current being supplied or absorbed. e load demand decreased to 2.08 A at t � 0.2 sec, and as shown in Figure 9, the surplus current absorbed by the battery to International Transactions on Electrical Energy Systems charge itself and the battery current is negative. Consequently, at t � 0.4 sec, the load current is increased again to 4.17 A, and at this point, the battery and the converter remain idle without any current. e load voltage is sustained at 48 V throughout, and Figure 10 shows the variation of SOC of battery and load voltage profile.

Hardware Implementation and Results.
e laboratory setup for the hardware implementation of the proposed work is shown in Figure 11.
A programmable DC power supply (Chroma-62020H-150S) from Chroma was employed as a PV source. ree LEM voltage sensors (LV25-P/SP213205) and two current sensors (LA55-P14316) were used to sense different voltages and currents. Outputs of sensors were given to dSPACE-1104 ADC channels with appropriate gain. is was used to implement the proposed control algorithm.
To capture the experimental results, RIGOL-DS1054 was used. e presented control algorithm was implemented by generating three gate pulses with an adjustable duty cycle using dSPACE-1104. A distinct gate pulse was given to switch the parallel-connected load to change the load. e experimental tests were carried out in fewer than two conditions: (i) change in the reference voltage and (ii) change in the load (boost and buck mode).

Reference Change.
e reference voltage is varied from 48 V to 36 V at a particular time, and it is shown that the output voltage v 0 is tracking the new reference of 36 V, as shown in Figure 12. Furthermore, it can be seen that the reference voltage has been restored to 48 V, and the controller tracks the output voltage in line with the reference voltage of 48 V.

Boost Mode (Discharging Mode).
e battery begins discharging through the converter in boost mode, which supplies the deficit power to keep the power balance and

Buck Mode (Charging Mode).
e battery begins charging through the converter in buck mode, absorbing excess power to keep the power balance and output voltage stable. Initially, the load current is 4.17 A, which the PV can handle perfectly. As a result, the battery stays uncharged, and no current is delivered or absorbed. As the load demand decreases, the battery absorbs the excess current to charge itself, as seen in Figure 14.

Comparison Analysis with Different Controllers
To analyze the performance quality of the proposed FF-DISMC controller, the transient and steady-state responses of system were observed with different controllers in terms of time-domain specifications (rise time, percentage undershoot, and settling time).
To examine the converter with PI controller (voltage mode control), the duty cycle to output voltage transfer function is derived from small-signal analysis around the steady-state operating point. It is observed that the unity feedback closed-loop system with that transfer function is unstable. Hence, a PI controller G vm (s) is designed. To tune the parameters of the PI controller, the stability boundary locus method [36] is used with a specified phase margin of 60°.
To analyze the BQZSDC with dual-loop PI controller (current mode controller), the two essential transfer functions, i.e., duty cycle to the inductor current (i L1 ) and duty cycle to the output voltage (v 0 ), are required. e BQZSDC's actual output voltage in the outer loop is compared to the reference DC link voltage, and the voltage error is sent to a voltage loop PI controller. e voltage loop PI generates a reference current signal for the inner loop. e current error is given to the current loop PI controller after comparing the reference current to the actual inductor current. is current PI controller regulates the duty cycle. e controllers are tuned in such a way that the bandwidth of the current control loop is greater than the outer voltage control loop bandwidth. As a result, the dynamics of the current loop are quicker than the outer voltage loop.
Because of unity feedback, the inner loop transfer function was observed as unstable. A PI controller was developed. e PI controller's parameter is tuned using the stability boundary locus approach. e PI controller G c (s) is as follows: To design the outer loop voltage PI controller, the voltage to current transfer function was derived from the analysis.
is transfer function's frequency response exhibits a constant gain in the low-frequency range, resulting in a substantial steady-state inaccuracy. A PI controller is designed to eliminate the steady-state error. e PI controller G v (s) is as follows: G v (s) � 0.02371 + 36.79 s .
e DISMC results were also compared to the basic integral SMC (ISMC); the number of control variables used in the ISMC and DISMC equations is the main difference. Only three control variables, x 1 , x 2 , and x 3 , are used in ISMC. e sliding surface equation in ISMC is as follows: where the control variables are as follows:  e equivalent control signal of ISMC control input obtained after analysis is as follows: e equivalent controller comprises a control signal v C and a ramp signal v ramp .
By considering all sliding mode conditions, the performances of the converter with all mentioned controllers with load change in both boost and buck mode are analyzed in Figures 15 and 16.
Tables 2 and 3 examine the transient response of BQZSDC with different controllers in boost and buck modes in terms of time-domain specifications.

Conclusion
In this work, an effective control (FF-DISMC) approach has been implemented for BQZSDC. In both buck and boost modes, energy management was achieved between PV, battery, and load. e controller was examined in depth, and its performance was analyzed in both charge (buck) and discharge (boost) modes. e controller met the voltage regulation and battery current regulatory requirements. e proposed controller's performance was also compared to that of other controllers, such as voltage mode, current mode, and single integral SMC, in terms of time-domain specifications such as rise, settling, and percentage peak overshoot. Further, the experimental validation of the proposed control technique on BQZSDC was implemented in both boost and buck modes of operation.

Symbols i L1 :
Current of inductor L 1 i L2 : Current of inductor L 2 i Load : Load current i C1 : Current of capacitor C 1 i C2 : Current of capacitor C 2 i C0 : Current of capacitor C 0 i 0 : Converter output current I L1ref : Reference current of L 1 v C1 : Voltage of capacitor C 1 v C2 : Voltage of capacitor C 2 v 0 : Voltage of output capacitor C 0 (load voltage) V b : Voltage of battery V ref : Reference load voltage u: Control input u eq : Controller equivalent control input R 0 : Load resistance r: ESR of capacitor C 2 x 1 , x 2 , x 3 , x 4 : Sliding variables S 1 , S 2 , S 3 : Switching devices S: Sliding surface α 1 , α 2 , α 3 , α 4 : Sliding coefficients k 1 , k 2 , k 3 : Controller gain constants K: Reference current gain p 1 , p 2 , p 3 , p 4 , p 5 , p 6 , p 7 : Coefficients of characteristic equation.

Data Availability
e data (converter parameters) used to support the findings of this study are included in the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.