# Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation

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## Abstract

**:**

## 1. Introduction

## 2. Background of the Proposed Solution

## 3. Proposed Sliding-Mode Controller

#### 3.1. Converter Model and Sliding Function Expressions

#### 3.2. Transversality Condition

- Stand-by stage (${i}_{b}=0$): since L and ${v}_{dc}$ are positive quantities, the parameter ${k}_{b}$ must be set as a positive quantity, as reported in (13).$$\begin{array}{c}\hfill \frac{d}{du}\left(\frac{d\mathrm{\Psi}}{dt}\right)=\frac{{k}_{b}\xb7{v}_{dc}}{L}>0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left\{\begin{array}{c}{i}_{b}=0\hfill \\ {k}_{b}>0\hfill \end{array}\right.\end{array}$$
- Charging stage (${i}_{b}<0$): since L, C, ${v}_{dc}$ and ${k}_{b}$ are positive quantities, the parameter ${k}_{p}$ must be set as a negative quantity, as reported in (14).$$\begin{array}{c}\hfill \frac{d}{du}\left(\frac{d\mathrm{\Psi}}{dt}\right)=\frac{{k}_{b}\xb7{v}_{dc}}{L}+\frac{{k}_{p}\xb7{i}_{b}}{C}>0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left\{\begin{array}{c}{i}_{b}<0\hfill \\ {k}_{b}>0\hfill \\ {k}_{p}<0\hfill \end{array}\right.\end{array}$$
- Discharging stage (${i}_{b}>0$): since L, C, ${v}_{dc}$ and ${k}_{b}$ are positive quantities, the parameter ${k}_{p}$ must fulfill the constraint presented in (15) to ensure the positive sign of the transversality.$$\begin{array}{c}\hfill \frac{d}{du}\left(\frac{d\mathrm{\Psi}}{dt}\right)>0\phantom{\rule{1.em}{0ex}},\phantom{\rule{1.em}{0ex}}\left\{\begin{array}{c}{i}_{b}>0\hfill \\ {k}_{b}>0\hfill \\ {k}_{p}>-\frac{C}{L}\xb7\frac{{v}_{b}}{{i}_{b}}\hfill \end{array}\right.\end{array}$$

#### 3.3. Reachability Conditions

#### 3.4. Equivalent Control

#### 3.5. Summary

## 4. Design of the Sliding-Mode Dynamics

#### 4.1. Selection of the Type of Dynamic Response

#### 4.2. Design of the Maximum Overshoot

#### 4.3. Design of the Settling Time

#### 4.4. Calculation of Parameters ${k}_{p}$ and ${k}_{i}$

#### 4.5. Summary

- Based on the load voltage requirements, define the maximum overshoot $\Delta {v}_{dc}$ and settling time ${t}_{s}$ (also specify the settling time band $\u03f5$).
- The parameter ${k}_{b}$ must be adapted continuously based on (32).
- Calculate the pole ${P}_{1}$ by solving (48) to provide the desired settling time ${t}_{s}$ for the band $\u03f5$.

## 5. Implementation and Operation Analysis

#### 5.1. Control Law and Switching Circuit

#### 5.2. Synthesis of the Sliding Function

#### 5.3. Speed Limitation under Perturbations

## 6. Design Example and Simulation Results

- Bus current step from 0 A to 1 A (5 ms): the bus voltage deviation produced under the control of the new solution is only $16\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from 1 A to 0 A (10 ms): the bus voltage deviation produced under the control of the new solution is only $6\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from 0 A to $-1$ A (15 ms): the bus voltage deviation produced under the control of the new solution is only $5\%$ of the deviation produced under the control of the solution in [15].
- Bus current step from $-1$ A to 2 A (20 ms): the bus voltage deviation produced under the control of the new solution is only $33\%$ of the deviation produced under the control of the solution in [15].

## 7. Experimental Validation

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Pillot, C. Battery Market Development for Consumer Electronics, Automotive, and Industrial: Materials Requirements & Trends. In Proceedings of the Batteries, Como, Italy, 10–14 June 2014; pp. 1–34. [Google Scholar]
- Huggins, R. Energy Storage, 2rd ed.; Springer International Publishing: Cham, Switzerland, 2016; pp. XXXVIII, 509. [Google Scholar]
- Krivik, P.; Baca, P. Electrochemical Energy Storage. In Energy Storage—Technologies and Applications; Zobaa, A.F., Ed.; InTech: Rijeka, Croatia, 2013; Chapter 3; p. 328. [Google Scholar]
- Xiao, Y.; Ge, X.; Zheng, Z. Analysis and Control of Flywheel Energy Storage Systems. In Energy Storage—Technologies and Applications; Zobaa, A.F., Ed.; InTech: Rijeka, Croatia, 2013; Chapter 6; p. 328. [Google Scholar]
- Putnam, C.S. The Mechanical Battery. 2016. Available online: https://www.damninteresting.com/the-mechanical-battery/ (accessed on 1 August 2017).
- Energy Technology Systems Analysis Program (IEA-ETSAP); International Renewable Energy Agency (IRENA). Thermal Energy Storage: Technology Brief; IRENA: Masdar City, UAE, 2013. [Google Scholar]
- Chen, H.; Zhang, X.; Liu, J.; Tan, C. Compressed Air Energy Storage. In Energy Storage—Technologies and Applications; Zobaa, A.F., Ed.; InTech: Rijeka, Croatia, 2013; Chapter 4; p. 328. [Google Scholar]
- Julien, C.; Mauger, A.; Vijh, A.; Zaghib, K. Lithium Batteries, 1st ed.; Springer International Publishing: Cham, Switzerland, 2016; pp. XV, 619. [Google Scholar]
- Ike, I.S.; Iyuke, S. Mathematical Modelling and Simulation of Supercapacitors. In Nanomaterials in Advanced Batteries and Supercapacitors, 1st ed.; Ozoemena, K.I., Chen, S., Eds.; Springer International Publishing: Cham, Switzerland, 2016; Chapter 15; pp. XV, 567. [Google Scholar]
- Zhang, Z.; Zhang, S.S. (Eds.) Rechargeable Batteries, 1st ed.; Green Energy and Technology; Springer International Publishing: Cham, Switzerland, 2015; pp. IX, 712. [Google Scholar]
- Cadex Electronics. BU-808b: What Causes Li-ion to Die?—Battery University; Cadex Electronics: Richmond, BC, Canada, 2017. [Google Scholar]
- Töpler, J.; Lehmann, J. (Eds.) Hydrogen and Fuel Cell, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2016; pp. XII, 281. [Google Scholar]
- Alam, M.J.E.; Muttaqi, K.M.; Sutanto, D. Effective Utilization of Available PEV Battery Capacity for Mitigation of Solar PV Impact and Grid Support With Integrated V2G Functionality. IEEE Trans. Smart Grid
**2016**, 7, 1562–1571. [Google Scholar] [CrossRef] - Wilson, A. The Growing Role of Energy Storage in Microgrids; Navigant: Boulder, CO, USA, 2016. [Google Scholar]
- Serna-Garcés, S.; Gonzalez Montoya, D.; Ramos-Paja, C. Sliding-Mode Control of a Charger/Discharger DC/DC Converter for DC-Bus Regulation in Renewable Power Systems. Energies
**2016**, 9, 245. [Google Scholar] [CrossRef] - Nwesaty, W.; Iuliana Bratcu, A.; Sename, O. Power sources coordination through multivariable linear parameter-varying/H∞ control with application to multi-source electric vehicles. IET Control Theory Appl.
**2016**, 10, 2049–2059. [Google Scholar] [CrossRef][Green Version] - López, J.; Seleme, S.; Donoso, P.; Morais, L.; Cortizo, P.; Severo, M. Digital control strategy for a buck converter operating as a battery charger for stand-alone photovoltaic systems. Sol. Energy
**2016**, 140, 171–187. [Google Scholar] [CrossRef] - Dominguez, X.; Camacho, O.; Leica, P.; Rosales, A. A fixed-frequency Sliding-mode control in a cascade scheme for the Half-bridge Bidirectional DC-DC converter. In Proceedings of the 2016 IEEE Ecuador Technical Chapters Meeting (ETCM), Guayaquil, Ecuador, 12–14 October 2016; pp. 1–6. [Google Scholar]
- Biswas, S.; Huang, L.; Vaidya, V.; Ravichandran, K.; Mohan, N.; Dhople, S.V. Universal Current-Mode Control Schemes to Charge Li-Ion Batteries Under DC/PV Source. IEEE Trans. Circuits Syst. I Regul. Pap.
**2016**, 63, 1531–1542. [Google Scholar] [CrossRef] - Marcos-Pastor, A.; Vidal-Idiarte, E.; Cid-Pastor, A.; Martinez-Salamero, L. Digital control of a unidirectional battery charger for electric vehicles. In Proceedings of the 2014 IEEE 15th Workshop on Control and Modeling for Power Electronics (COMPEL), Santander, Spain, 22–25 June 2014; pp. 1–6. [Google Scholar]
- Na, W.; Quattum, B.; Publes, A.; Maddipatla, V. A sliding mode control based multi-functional power converter for electric vehicles and energy applications. In Proceedings of the 2013 International Electric Machines & Drives Conference, Chicago, IL, USA, 12–15 May 2013; pp. 742–746. [Google Scholar]
- Etxeberria, A.; Vechiu, I.; Camblong, H.; Vinassa, J.M. Comparison of Sliding Mode and PI Control of a Hybrid Energy Storage System in a Microgrid Application. Energy Procedia
**2011**, 12, 966–974. [Google Scholar] [CrossRef] - Aamir, M.; Mekhilef, S. An Online Transformerless Uninterruptible Power Supply (UPS) System with a Smaller Battery Bank for Low-Power Applications. IEEE Trans. Power Electron.
**2017**, 32, 233–247. [Google Scholar] [CrossRef] - Philip, J.; Jain, C.; Kant, K.; Singh, B.; Mishra, S.; Chandra, A.; Al-Haddad, K. Control and Implementation of a Standalone Solar Photovoltaic Hybrid System. IEEE Trans. Ind. Appl.
**2016**, 52, 3472–3479. [Google Scholar] [CrossRef] - Khayamy, M.; Ojo, O.; Sota, E. Non-linear controller approach for an autonomous battery-assisted photovoltaic system feeding an AC load with a non-linear component. IET Renew. Power Gener.
**2014**, 8, 838–848. [Google Scholar] [CrossRef] - Daud, M.Z.; Mohamed, A.; Hannan, M.A. An Optimal Control Strategy for DC Bus Voltage Regulation in Photovoltaic System with Battery Energy Storage. Sci. World J.
**2014**, 2014. [Google Scholar] [CrossRef] [PubMed] - Venayagamoorthy, G.K.; Sharma, R.K.; Gautam, P.K.; Ahmadi, A. Dynamic Energy Management System for a Smart Microgrid. IEEE Trans. Neural Netw. Learn. Syst.
**2016**, 27, 1643–1656. [Google Scholar] [CrossRef] [PubMed] - Shen, J.; Khaligh, A. A Supervisory Energy Management Control Strategy in a Battery/Ultracapacitor Hybrid Energy Storage System. IEEE Trans. Transp. Electrif.
**2015**, 1, 223–231. [Google Scholar] [CrossRef] - Dubois, M.R.; Desrochers, A.; Denis, N. Fuzzy-based blended control for the energy management of a parallel plug-in hybrid electric vehicle. IET Intell. Transp. Syst.
**2015**, 9, 30–37. [Google Scholar] - Han, J.; Khushalani-Solanki, S.; Solanki, J.; Liang, J. Adaptive Critic Design-Based Dynamic Stochastic Optimal Control Design for a Microgrid With Multiple Renewable Resources. IEEE Trans. Smart Grid
**2015**, 6, 2694–2703. [Google Scholar] [CrossRef] - Yoo, C.H.; Chung, I.Y.; Lee, H.J.; Hong, S.S. Intelligent Control of Battery Energy Storage for Multi-Agent Based Microgrid Energy Management. Energies
**2013**, 6, 4956–4979. [Google Scholar] [CrossRef] - Lin, F.J.; Hung, Y.C.; Huang, M.S.; Kuan, C.H.; Wang, S.L.; Lee, Y.D. Takagi-Sugeno-Kang type probabilistic fuzzy neural network control for grid-connected LiFePO4 battery storage system. IET Power Electron.
**2013**, 6, 1029–1040. [Google Scholar] [CrossRef] - Jisha, L.; Powlly Thomas, A.; Srivastava, S. Sliding Mode Controller Vs PID Controller For Induction Motor—A Comparative Study. In Proceedings of the International Conference on Current Trends in Engineering, Science and Technology (ICCTEST-2017), Mumbai, India, 5–7 January 2017; Grenze Scientific Society: Trivandrum, India, 2017; pp. 1082–1088. [Google Scholar]
- Raoufi, R. SMC vs PID Feedback Control; Design Engineering: Edmonton, Canada, 2011. [Google Scholar]
- White, A.; Zhu, G.; Choi, J. Linear Parameter-Varying Control for Engineering Applications; Springer Briefs in Electrical and Computer Engineering; Springer: London, UK, 2013. [Google Scholar]
- Granados-Luna, T.R.; Araujo-Vargas, I.; Perez-Pinal, F.J. Sample-Data Modeling of a Zero Voltage Transition DC-DC Converter for On-Board Battery Charger in EV. Math. Probl. Eng.
**2014**, 2014. [Google Scholar] [CrossRef] - Pan, L.; Zhang, C. A High Power Density Integrated Charger for Electric Vehicles with Active Ripple Compensation. Math. Probl. Eng.
**2015**, 2015. [Google Scholar] [CrossRef] - Liu, J.; Zhao, Y.; Geng, B.; Xiao, B. Adaptive Second Order Sliding Mode Control of a Fuel Cell Hybrid System for Electric Vehicle Applications. Math. Probl. Eng.
**2015**, 2015. [Google Scholar] [CrossRef] - Smuts, J.F. Advanced Regulatory Control. In Process Control for Practitioners: How to Tune PID Controllers and Optimize Control Loops; OptiControls Inc.: League City, TX, USA, 2011; Chapter 8; p. 315. [Google Scholar]
- Kaya, I.; Tan, N.; Atherton, D.P. Improved cascade control structure for enhanced performance. J. Process Control
**2007**, 17, 3–16. [Google Scholar] [CrossRef] - Marlin, T.E. Cascade Control. In Process Control: Designing Processes and Control Systems for Dynamic Performance, 2nd ed.; McGraw-Hill: New York, NY, USA, 2000; Chapter 14; p. 1017. [Google Scholar]
- Sira-Ramírez, H. Sliding Motions in Bilinear Switched Networks. IEEE Trans. Circuits Syst.
**1987**, 34, 919–933. [Google Scholar] [CrossRef] - Bacha, S.; Munteanu, I.; Bratcu, A.I. Power Electronic Converters Modeling and Control; Advanced Textbooks in Control and Signal Processing; Springer: London, UK, 2014; p. 469. [Google Scholar]
- Erickson, R.W.; Maksimović, D. Fundamentals of Power Electronics, 2rd ed.; Springer: Boston, MA, USA, 2001; pp. XXI, 883. [Google Scholar]
- Gonzalez Montoya, D.; Ramos-Paja, C.A.; Giral, R. Improved Design of Sliding-Mode Controllers Based on the Requirements of MPPT Techniques. IEEE Trans. Power Electron.
**2016**, 31, 235–247. [Google Scholar] [CrossRef] - Tan, S.C.; Lai, Y.M.; Tse, C.K. Sliding Mode Control of Switching Power Converters Techniques and Implementation; CRC Press Taylor & Francis Group: Boca Raton, FL, USA, 2012; p. 285. [Google Scholar]
- Ogata, K. Modern Control Engineering, 5th ed.; Prentice Hall PTR: Upper Saddle River, NJ, USA, 2010; p. 905. [Google Scholar]
- Boiko, I.; Fridman, L.; Pisano, A.; Usai, E. A Comprehensive Analysis of Chattering in Second Order Sliding Mode Control Systems. In Modern Sliding Mode Control Theory; Lecture Notes in Control and Information Sciences; Bartolini, G., Fridman, L., Pisano, A., Usai, E., Eds.; Springer: Berlin/Heidelberg, Germany, 2008; Volume 375, Chapter 2; p. 470. [Google Scholar]
- ST Microelectronics. TS555—Low Power Single CMOS Timer—STMicroelectronics; ST Microelectronics: Geneva, Switzerland, 2017. [Google Scholar]
- MTEK. MT12330HR (12V35Ah); Technical Report; MTEK: Medellín, Colombia, 2009. [Google Scholar]
- Kepco, I. Quick Start Guide BOP 1kW-GL; Technical Report; Kepco, Inc.: Flushing, NY, USA, 2013. [Google Scholar]
- Analog Devices. High Voltage, Bidirectional Current Shunt Monitor—AD8210; Technical Report; Analog Devices: Norwood, MA, USA, 2013. [Google Scholar]
- Texas Instruments Inc. TMS320F2833x, TMS320F2823x Digital Signal Controllers (DSCs); Technical Report; Texas Instruments Inc.: Dallas, TX, USA, 2016. [Google Scholar]
- Microchip Technology Inc. MCP4802/4812/4822; Technical Report; Microchip Technology Inc.: Chandler, AZ, USA, 2015. [Google Scholar]
- Intersil Americas Inc. HIP4081A, 80V High Frequency H-Bridge Driver; Technical Report; Intersil Americas Inc.: Milpitas, CA, USA, 2007. [Google Scholar]

**Figure 4.**Simulation of the controller presented in [15].

**Figure 5.**Proposed structure of a sliding-mode controller with improved disturbance rejection for the charger/discharger.

**Figure 8.**Simulation of ${G}_{dc}\left(s\right)$ for $m=0.0765$ to ensure that $\Delta {v}_{dc}=5\%$.

**Figure 10.**Simulation of ${G}_{dc}\left(s\right)$ with values of ${P}_{1}$ to ensure that ${t}_{s}=3$ ms for a settling time band $\u03f5=2\%$.

**Figure 11.**Switching circuit implementing the control law in (51).

**Figure 17.**Simulation of both the proposed SMC and the SMC without measuring ${i}_{dc}$ presented in [15].

**Figure 19.**Experimental platform. (

**a**) Schematic diagram of the experimental platform; (

**b**) Experimental devices.

**Figure 20.**Experimental results for 1 A steps in the bus current. (

**a**) DC bus voltage regulation with the SMC reported in [15]; (

**b**) DC bus voltage regulation with the proposed SMC.

$\mathbf{\Delta}{\mathit{v}}_{\mathit{dc}}$ | m | ${\mathit{P}}_{\mathbf{1}}$ | ${\mathit{P}}_{\mathbf{2}}$ |
---|---|---|---|

$5\%$ | 13.0719 | $473.7$ rad/s | $6192.2$ rad/s |

$7\%$ | 7.8128 | $664.4$ rad/s | $5190.8$ rad/s |

$9\%$ | 4.9373 | $847.1$ rad/s | $4182.4$ rad/s |

$11\%$ | 3.0858 | $1057.6$ rad/s | $3263.5$ rad/s |

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**MDPI and ACS Style**

Serna-Garcés, S.I.; González Montoya, D.; Ramos-Paja, C.A. Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation. *Energies* **2018**, *11*, 594.
https://doi.org/10.3390/en11030594

**AMA Style**

Serna-Garcés SI, González Montoya D, Ramos-Paja CA. Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation. *Energies*. 2018; 11(3):594.
https://doi.org/10.3390/en11030594

**Chicago/Turabian Style**

Serna-Garcés, Sergio Ignacio, Daniel González Montoya, and Carlos Andrés Ramos-Paja. 2018. "Control of a Charger/Discharger DC/DC Converter with Improved Disturbance Rejection for Bus Regulation" *Energies* 11, no. 3: 594.
https://doi.org/10.3390/en11030594