# An IDA-PBC Design with Integral Action for Output Voltage Regulation in an Interleaved Boost Converter for DC Microgrid Applications

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## Abstract

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## 1. Introduction

- The application of the IDA-PBC controller to the interleaved boost converter for output voltage regulation in DC microgrids with variable injected/demanded current: to improve the IDA-PBC design’s performance, an integral action is added using the passive output of the system that does not affect the stability properties in closed-loop and allows eliminating the steady-state errors introduced by possible unmodeled dynamics;
- The proposed controller owns the advantage of not depending on the parameters of the interleaved boost converter which makes its robustness parametric variations.
- Select the current references through the inductor to maintain a balanced operation at each branch for positive and negative references.

## 2. Average Modeling for an Interleaved Boost Converter

**Remark**

**1.**

## 3. IDA-PBC Design

#### 3.1. Assignable Equilibrium Point

**Remark**

**2.**

#### 3.2. Classical IDA-PBC Design

**Remark**

**3.**

#### 3.3. IDA-PBC Redesign with Integral Action

**Remark**

**4.**

## 4. Numerical Validation

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lana, A.; Mattsson, A.; Nuutinen, P.; Peltoniemi, P.; Kaipia, T.; Kosonen, A.; Aarniovuori, L.; Partanen, J. On Low-Voltage DC Network Customer-End Inverter Energy Efficiency. IEEE Trans. Smart Grid
**2014**, 5, 2709–2717. [Google Scholar] [CrossRef] - Montoya, O.D.; Gil-González, W.; Serra, F.M.; Angelo, C.H.D.; Hernández, J.C. Global Optimal Stabilization of MT-HVDC Systems: Inverse Optimal Control Approach. Electronics
**2021**, 10, 2819. [Google Scholar] [CrossRef] - Garces, A. Uniqueness of the power flow solutions in low voltage direct current grids. Electr. Power Syst. Res.
**2017**, 151, 149–153. [Google Scholar] [CrossRef] - Justo, J.J.; Mwasilu, F.; Lee, J.; Jung, J.W. AC-microgrids versus DC-microgrids with distributed energy resources: A review. Renew. Sustain. Energy Rev.
**2013**, 24, 387–405. [Google Scholar] [CrossRef] - Lotfi, H.; Khodaei, A. AC Versus DC Microgrid Planning. IEEE Trans. Smart Grid
**2017**, 8, 296–304. [Google Scholar] [CrossRef] - Magaldi, G.L.; Serra, F.M.; de Angelo, C.H.; Montoya, O.D.; Giral-Ramírez, D.A. Voltage Regulation of an Isolated DC Microgrid with a Constant Power Load: A Passivity-based Control Design. Electronics
**2021**, 10, 2085. [Google Scholar] [CrossRef] - Serra, F.M.; Angelo, C.H.D. Control of a battery charger for electric vehicles with unity power factor. Trans. Energy Syst. Eng. Appl.
**2021**, 2, 32–44. [Google Scholar] [CrossRef] - Solsona, J.A.; Jorge, S.G.; Busada, C.A. Nonlinear Control of a Buck Converter Which Feeds a Constant Power Load. IEEE Trans. Power Electron.
**2015**, 30, 7193–7201. [Google Scholar] [CrossRef] - Salimi, M.; Siami, S. Cascade nonlinear control of DC-DC buck/boost converter using exact feedback linearization. In Proceedings of the 2015 4th International Conference on Electric Power and Energy Conversion Systems (EPECS), Sharjah, United Arab Emirates, 24–26 November 2015; IEEE: Piscataway, NJ, USA, 2015. [Google Scholar] [CrossRef]
- Gil-González, W.; Montoya, O.D.; Restrepo, C.; Hernández, J.C. Sensorless Adaptive Voltage Control for Classical DC-DC Converters Feeding Unknown Loads: A Generalized PI Passivity-Based Approach. Sensors
**2021**, 21, 6367. [Google Scholar] [CrossRef] - Ramos-Paja, C.A.; Gonzalez-Motoya, D.; Villegas-Seballos, J.P.; Serna-Garces, S.I.; Giral, R. Sliding-mode controller for a photovoltaic system based on a Cuk converter. Int. J. Electr. Comput. Eng. (IJECE)
**2021**, 11, 2027. [Google Scholar] [CrossRef] - Jin, P.; Li, Y.; Li, G.; Chen, Z.; Zhai, X. Optimized hierarchical power oscillations control for distributed generation under unbalanced conditions. Appl. Energy
**2017**, 194, 343–352. [Google Scholar] [CrossRef] [Green Version] - Iskender, I.; Genc, N. Power Electronic Converters in DC Microgrid. In Power Systems; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 115–137. [Google Scholar] [CrossRef]
- Quintero, C.E.; Pérez, S.A.; Ceballos, J.P.V.; González-Montoya, D.; Garcés, S.S. Design and Digital Control of an Interleaved Boost Converter for Battery Charge/Discharge. Tecnológicas
**2021**, 24, e1556. (In Spanish) [Google Scholar] [CrossRef] - He, L.; Lin, Z.; Tan, Q.; Lu, F.; Zeng, T. Interleaved High Step-Up Current Sharing Converter with Coupled Inductors. Electronics
**2021**, 10, 436. [Google Scholar] [CrossRef] - Hausberger, T.; Kugi, A.; Eder, A.; Kemmetmüller, W. High-speed nonlinear model predictive control of an interleaved switching DC/DC-converter. Control. Eng. Pract.
**2020**, 103, 104576. [Google Scholar] [CrossRef] - Cervantes, I.; Mendoza-Torres, A.; Garcia-Cuevas, A.; Perez-Pinal, F. Switched control of interleaved converters. In Proceedings of the 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA, 7–11 September 2009; IEEE: Piscataway, NJ, USA, 2009. [Google Scholar] [CrossRef]
- Kumar, S.S.; Kanimozhi, G. A nonlinear control technique for interleaved boost converter. In Proceedings of the 2016 10th International Conference on Intelligent Systems and Control (ISCO), Coimbatore, India, 7–8 January 2016; IEEE: Piscataway, NJ, USA, 2016. [Google Scholar] [CrossRef]
- Cid-Pastor, A.; Giral, R.; Calvente, J.; Utkin, V.I.; Martinez-Salamero, L. Interleaved Converters Based on Sliding-Mode Control in a Ring Configuration. IEEE Trans. Circuits Syst. I Regul. Pap.
**2011**, 58, 2566–2577. [Google Scholar] [CrossRef] - Tiwari, A.; Jaga, O.; Soni, S.S. Sliding mode controller based interleaved boost converter for fuel cell system. In Proceedings of the 2017 Recent Developments in Control, Automation & Power Engineering (RDCAPE), Noida, India, 26–27 October 2017; IEEE: Piscataway, NJ, USA, 2017. [Google Scholar] [CrossRef]
- Gkizas, G.; Amanatidis, C.; Yfoulis, C.; Stergiopoulos, F.; Giaouris, D.; Ziogou, C.; Voutetakis, S.; Papadopoulou, S. State-feedback control of an interleaved DC-DC boost converter. In Proceedings of the 2016 24th Mediterranean Conference on Control and Automation (MED), Athens, Greece, 21–24 June 2016; IEEE: Piscataway, NJ, USA, 2016. [Google Scholar] [CrossRef]
- González, A.; López-Erauskin, R.; Gyselinck, J. Analysis, modeling, control and operation of an interleaved three-port boost converter for DMPPT systems including PV and storage at module level. Heliyon
**2019**, 5, e01402. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Olmos-Lopez, A.; Guerrero, G.; Arau, J.; Aguilar, C.; Yris, J.C. Passivity-based control for current sharing in PFC interleaved boost converters. In Proceedings of the 2011 Twenty-Sixth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA, 6–11 March 2011; IEEE: Piscataway, NJ, USA, 2011. [Google Scholar] [CrossRef]
- Zhou, H.; Khambadkone, A.M.; Kong, X. A Passivity Based Control with Augmented Integration for an Interleaved Current Fed Full Bridge Converter as a Front End for Fuel Cell Source. In Proceedings of the 2007 IEEE Industry Applications Annual Meeting, New Orleans, LA, USA, 23–27 September 2007; IEEE: Piscataway, NJ, USA, 2007. [Google Scholar] [CrossRef]
- Bharathi, M.; Kirubakaran, D. Solar powered closed-loop controlled fuzzy logic-based three-stage interleaved DC-DC boost converter with an inverter. Int. J. Adv. Intell. Paradig.
**2016**, 8, 140. [Google Scholar] [CrossRef] - Sunarno, E.; Sudiharto, I.; Nugraha, S.D.; Qudsi, O.A.; Eviningsih, R.P.; Raharja, L.P.S.; Arifin, I.F. A Simple And Implementation of Interleaved Boost Converter For Renewable Energy. In Proceedings of the 2018 International Conference on Sustainable Energy Engineering and Application (ICSEEA), Tangerang, Indonesia, 1–2 November 2018; IEEE: Piscataway, NJ, USA, 2018. [Google Scholar] [CrossRef]
- Barhoumi, E.; Belgacem, I.B.; Khiareddine, A.; Zghaibeh, M.; Tlili, I. A Neural Network-Based Four Phases Interleaved Boost Converter for Fuel Cell System Applications. Energies
**2018**, 11, 3423. [Google Scholar] [CrossRef] [Green Version] - Gonzalez, W.J.G.; Bocanegra, S.Y.; Serra, F.M.; Bueno-López, M.; Magaldi, G.L. Control Methods for Single-phase Voltage Supply with VSCs to Feed Nonlinear Loads in Rural Areas. Trans. Energy Syst. Eng. Appl.
**2020**, 1, 33–47. [Google Scholar] [CrossRef] - Serra, F.M.; Angelo, C.H.D.; Forchetti, D.G. Interconnection and damping assignment control of a three-phase front end converter. Int. J. Electr. Power Energy Syst.
**2014**, 60, 317–324. [Google Scholar] [CrossRef] - Herrera-Pérez, J.J.; Garcés-Ruiz, A. Análisis de estabilidad de convertidores de segundo orden con la metodología de optimización de suma de polinomios cuadráticos. Trans. Energy Syst. Eng. Appl.
**2020**, 1, 49–58. (In Spanish) [Google Scholar] [CrossRef] - Serra, F.M.; Angelo, C.H.D. IDA-PBC controller design for grid connected Front End Converters under non-ideal grid conditions. Electr. Power Syst. Res.
**2017**, 142, 12–19. [Google Scholar] [CrossRef] - Donaire, A.; Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica
**2009**, 45, 1910–1916. [Google Scholar] [CrossRef] - Asadi, F.; Eguchi, K. Simulation of Power Electronics Converters Using PLECS
^{®}; Elsevier: Amsterdam, The Netherlands, 2020. [Google Scholar] [CrossRef] - Frivaldsky, M.; Morgos, J.; Prazenica, M.; Takacs, K. System Level Simulation of Microgrid Power Electronic Systems. Electronics
**2021**, 10, 644. [Google Scholar] [CrossRef] - Morales, J.A.; Castro, M.A.; Garcia, D.; Higuera, C.; Sandoval, J. IDA-PBC Controller Tuning Using Steepest Descent. In Numerical and Evolutionary Optimization—NEO 2017; Springer International Publishing: Berlin/Heidelberg, Germany, 2018; pp. 158–170. [Google Scholar] [CrossRef]

**Figure 4.**The dynamic response of output voltage of the interleaved boost converter under different DC current steps.

**Figure 5.**The dynamic response of currents associated with the interleaved boost converter under different DC current steps.

**Figure 6.**The dynamic response of control inputs with the interleaved boost converter under different DC current steps.

**Figure 8.**The dynamic response of output voltage of the interleaved boost converter under different DC voltage and current steps.

**Figure 9.**The dynamic response of currents associated with the interleaved boost converter under different DC voltage and current steps.

**Figure 10.**The dynamic response of control inputs with the interleaved boost converter under different DC voltage and current steps.

Element | Variable | Value | Element | Variable | Value | Element | Variable | Value |
---|---|---|---|---|---|---|---|---|

Battery Voltage | ${v}_{b}$ | 24 V | Bus Voltage | ${v}_{dc}$ | 48 V | Inductor | ${L}_{1}$, ${L}_{2}$ | 330 mH |

Switching frequency | ${f}_{q}$ | 2 kHz | Capacitor | C | 44 $\mathsf{\mu}$F |

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**MDPI and ACS Style**

Montoya, O.D.; Serra, F.M.; Gil-González, W.; Asensio, E.M.; Bosso, J.E.
An IDA-PBC Design with Integral Action for Output Voltage Regulation in an Interleaved Boost Converter for DC Microgrid Applications. *Actuators* **2022**, *11*, 5.
https://doi.org/10.3390/act11010005

**AMA Style**

Montoya OD, Serra FM, Gil-González W, Asensio EM, Bosso JE.
An IDA-PBC Design with Integral Action for Output Voltage Regulation in an Interleaved Boost Converter for DC Microgrid Applications. *Actuators*. 2022; 11(1):5.
https://doi.org/10.3390/act11010005

**Chicago/Turabian Style**

Montoya, Oscar Danilo, Federico Martin Serra, Walter Gil-González, Eduardo Maximiliano Asensio, and Jonathan Emmanuel Bosso.
2022. "An IDA-PBC Design with Integral Action for Output Voltage Regulation in an Interleaved Boost Converter for DC Microgrid Applications" *Actuators* 11, no. 1: 5.
https://doi.org/10.3390/act11010005