# Quantitative Design for the Battery Equalizing Charge/Discharge Controller of the Photovoltaic Energy Storage System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Adopted MPPT Method

## 3. The Adopted Equalizing Charge/Discharge Architecture

_{H}

_{1}, S

_{H}

_{2}, S

_{L}

_{1}and S

_{L}

_{2}) to obtain the characteristics required for zero-voltage switching (ZVS) and zero-current switching (ZCS). Therefore, when using the soft switching function, the converter must be operated under heavy load conditions to achieve higher conversion efficiency. When operating under a lighter load (under 150 W), because the inductive current is under the discontinuous conduction mode, it may prevent the resonance circuit from smoothly executing the resonance. As a result, limited efficiency can be noted for the soft switching converter only, and the efficiency will become even lower than the conventional hard switching converter.

## 4. Quantitative Design of the Bidirectional Buck–Boost Soft-Switching Converter Controller

#### 4.1. Quantitative Design of the Current Controller

_{L}and S

_{H}are complementarily controlled, the results derived from both the boost mode or the buck mode are the same; therefore, the analysis process below is derived from the dynamic mode of the converter only under the boost mode.

_{L}—that is, the peak value of i

_{L}at full load ${({\widehat{I}}_{L})}_{\mathit{max}}$ is used to determine the on-time ${t}_{D}$ of the auxiliary switch, and ${t}_{D}$ is usually 5~10% of the switching period T [6]. In addition, a margin time ${t}_{\epsilon}$ is required to obtain a reliable t

_{D}, so here, we set ${t}_{D}$ = 0.1 T = 4 µs, and ${t}_{\epsilon}$ = 0.01 T = 0.4 μs, and then used Equation (1) to derive a maximum resonance inductance value L

_{a}

_{1}= L

_{a}

_{2}= 18 μH, so we can select a resonance inductance value smaller than 18μH, which would be acceptable. In addition, the selected switching component IGBT-IXGH48N60C3D1 has a stray capacitance of 202pF, so the resonance capacitors C

_{a}

_{1}and C

_{a}

_{2}can be replaced by stray capacitors:

#### 4.1.1. Conducting State of Low-Voltage Side Switch S_{L} ($0\le t\le dT$)

_{L}is conducting, the high-voltage side switch S

_{H}is in a cut-off state at this time; the equivalent circuit is shown in Figure 4. The state equation for the converter can be represented by:

#### 4.1.2. Cut-Off State of Low-Voltage Side Switch S_{L} ($dT\le t\le T$)

_{L}is in a cut-off state, the high-voltage side switch S

_{H}is conducting; the equivalent circuit can be presented in Figure 5. The load in the equivalent circuit is pure resistance R

_{Bus}. Then, the state equation can be obtained in Equation (3).

_{L}to obtain the average over one period, where Equation (2) is multiplied by dT, plus Equation (3) multiplied by (1 − d) T and divided by T, to arrive at:

_{Bat}, ${\mathrm{V}}_{{C}_{Bus}}$, V

_{Bus}, I

_{L}, ${I}_{{S}_{H}}$ and D are the values for the respective operating points; the perturbation signal is then substituted into Equation (4) to arrive at Equation (5) after rearrangement.

#### 4.1.3. Steady State

#### 4.1.4. Dynamic State

_{L}, V

_{Bus}, ${I}_{{S}_{H}}$, D, ${V}_{{C}_{Bus}}$) is:

_{c}, is smaller than the 1/2 f

_{s}[27] of the switching frequency, as shown in Equation (14):

_{Pi}. Then, when analyzing ${K}_{Ii}=\mathrm{10,000}$ with MATLAB software, the Bode plot from THE loop gain frequency response presented in different K

_{Pi}are shown in Figure 7. After analysis, the conditions which arrive at K

_{Pi}are:

#### 4.2. Dynamic Mode Estimation

_{v}(K

_{v}= 0.01 is used here), G

_{cv}(s) is the voltage controller, G

_{p}(s) is the transfer function of the bidirectional soft-switching converter, and K

_{pv}is the voltage conversion coefficient during DC-link power perturbation. In order to find the dynamic mode for the converter to facilitate the design of the DC-link voltage controller, this paper will carry out the dynamic mode estimation of the converter using step response [27].

- (a)
- When carrying out estimation mode, the proportional controller is adopted as the voltage controller, making G
_{cv}(s) = K_{P}= 10, then selecting an operating point (V_{Bus}= 180 V, P = 300 W), setting this system operation as closed-loop control. This paper hypothesizes that the dynamic model of the bidirectional buck–boost converter can be derived using the step response estimation method. Therefore, the parameter K_{P}of the proportional controller is given at will as long as the step response is without overshoot. - (b)
- Given a step command ($\Delta {v}_{\mathrm{Bus}}^{*}=0.6$, K
_{v}= 0.01, voltage V_{Bus}at high-voltage side increases from 180 V→240 V), then the measured variable waveform for the DC-link V_{Bus}voltage is shown in Figure 9; its steady-state voltage is at 220 V. The step command change Δv^{*}_{Bus}is also given arbitrarily, and K_{v}is the conversion factor of the voltage sensor. - (c)
- Under the same operating conditions, given a set sunlight variation, so the output power variation is $\Delta {\mathrm{P}}_{\mathrm{p}v}=100\mathrm{W}$, which is P
_{pv}from 1000 W→900 W, the measured DC-link voltage V_{Bus}variable waveform is shown in Figure 10, and the steady-state voltage is at 173 V. - (d)
- The transfer functions for $\Delta {v}_{\mathit{Bus}}^{}$ to $\Delta {v}_{\mathit{Bus}}^{*}$ and $\Delta {v}_{\mathit{Bus}}^{}$ to $\Delta {P}_{\mathit{pv}}$ can be derived from Figure 8 as shown in Equations (17) and (18), respectively.

- (e)
- From the DC-link voltage step response shown in Figure 9, the steady-state value and the time to reach $(1-{e}^{-1})$ times the steady-state value can be observed and the parameters can be calculated as ${c}_{1}$ = 53.77 and r = 80.65.
- (f)
- The steady-state response of power step change can be obtained against DC-link voltage from Figure 10 and calculate ${c}_{2}$ = 0.056 and K
_{pv}= 0.00967 from Equation (18). - (g)
- a = 26.88 and b = 537.7 can be estimated from Equation (17); therefore, the transfer function G
_{p}(s) of the bidirectional soft-switching converter can be written as:

#### 4.3. Quantitative Design of the Voltage Controller

_{cv}(s) adopts the P-I controller shown in Equation (20). The two parameters ${K}_{{P}_{v}}$ and K

_{Pv}in Figure 11 are the conversion factor between the power and voltage and the proportional parameter of the P-I controller for the DC link voltage, respectively. Therefore, these two parameters not only have different symbols, but also have different meaning.

## 5. Test Results

#### 5.1. Response Performance Comparison between Quantitative Design and Traditional P-I Controller

_{r}that occur due to step variation cannot be regulated. Thus, this paper has designed controllers that meet the selected specifications via the quantitative method.

_{Bus}= 240 V and load P = 300 W).

- (1)
- Non-overshoot.
- (2)
- No steady-state error.
- (3)
- From the maximum voltage drop ${\widehat{v}}_{Bus,max}=0.1\mathrm{V}/\mathrm{W}$ induced by the step sunlight variation (that is, photovoltaic module array output power variation) (meaning $100\mathrm{W}\to 10\mathrm{V}$ ).
- (4)
- From the voltage recovery time induced by the step sunlight variation ${t}_{r}=0.5s$.

^{2}drops to 900 W/m

^{2}. From the figure, we see that lowering the insolation resulted in lowering the output power for the photovoltaic module array to incur the sudden dropping of DC-link voltage. Because the PI controller parameters are designed by the quantitative method according to the preset performance specifications (including the maximum voltage drop of DC-link voltage and its recovery time), DC-link voltage is restored to the set 240 V for about 0.5 s. Indicated in Figure 15a is the waveform measured by the conventional PI controller under the same conditions and its recovery time will be 0.8 s. As such, there is a 0.3 s difference in response speed between both of them. Likewise, when the insolation rises to 1000 W/m

^{2}from 900 W/m

^{2}, the DC-link voltage suddenly increases due to the output power in the photovoltaic module array. In Figure 14b, we see that the quantitative PI controller allows the DC-link voltage to restore the set 240 V in about 0.5 s. Shown in Figure 15b is the waveform measured by the conventional PI controller under the same conditions and its restoration time is about 0.8 s. Same as above, there is a 0.3 s difference in the response speed between both of them. If the PI controller parameters are designed by a quantitative method according to the preset performance specifications, it allows the DC-link voltage to restore to the set 240 V more quickly under the specified maximum voltage drop.

#### 5.2. Response Test for the Photovoltaic Array Combined with the Equalizing Charge/Discharge Controller

_{pv}) is lower than the load power, the battery will discharge as an auxiliary power supply; conversely, it can be observed from Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25 that if the PVMA output power (P

_{pv}) is higher than the load power, the battery will charge to keep the DC-link voltage (V

_{Bus}) constant. The greater the voltage difference between the two batteries, the time required for charge/discharge will be comparatively longer, and the discharging current for the battery with more energy storage is greater during the initial discharge; on the other hand, during the initial charge, the charging current for the battery with more energy storage is smaller.

_{sc}and I

_{mp}present more prominent amplitude change but that of V

_{oc}and V

_{mp}is not so prominent.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Botelho, A.; Pinto, L.M.C.; Louren-Gomes, L.; Valente, M.; Social, S. Sustainability of Renewable Energy Sources in Electricity Production: An Application of the Contingent Valuation Method. Sustain. Cities Societ.
**2016**, 26, 429–437. [Google Scholar] [CrossRef] - Okonkwo, P.C.; Mansir, I.B.; Barhoumi, E.M.; Emori, W.; Radwan, A.B.; Shakoor, R.A.; Uzoma, P.C.; Pugalenthi, M.R. Utilization of Renewable Hybrid Energy for Refueling Station in Al-Kharj, Saudi Arabia. Int. J. Hhydr. Energy
**2022**, 47, 22273–22284. [Google Scholar] [CrossRef] - Alhousni1, F.K.; Ismail1, F.B.; Okonkwo, P.C.; Mohamed, H.; Okonkwo, B.O.; Al-ShahriA, O.A. Review of PV Solar Energy System Operations and Applications in Dhofar Oman. AIMS Energy
**2022**, 10, 858–884. [Google Scholar] [CrossRef] - Pérez-Deniciaa, E.; Fernández-Luqueñob, F.; Vilariño-Ayalac, D.; Montaño-Zetinad, L.M.; Maldonado-López, L.A. Renewable Energy Sources for Electricity Generation in Mexico: A Review. Renew. Sust. Energy Rev.
**2017**, 78, 597–613. [Google Scholar] [CrossRef] - Beitelmal, W.H.; Okonkwo, P.C.; Housni, F.A.; Grami, S.; Emori, W.; Uzoma, P.C.; Das, B.K. Renewable Energy as a Source of Electricity for Murzuq Health Clinic during COVID-19. MRS Energy Sustain.
**2022**, 9, 79–93. [Google Scholar] [CrossRef] - Chao, K.H.; Huang, B.Z.; Jian, J.J. An Energy Storage System Composed of Photovoltaic Arrays and Batteries with Uniform Charge/Discharge. Energies
**2022**, 15, 2883. [Google Scholar] [CrossRef] - Ramireddy, K.; Hirpara, Y.; Kumar, Y.V.P. Transient performance analysis of buck boost converter using various PID gain tuning methods. In Proceedings of the 12th International Conference on Computational Intelligence and Communication Networks (CICN), Bhimtal, India, 25–26 September 2020; pp. 321–326. [Google Scholar]
- Lei, W.; Li, C.; Chen, M.Z.Q. Robust Adaptive Tracking Control for Quadrotors by Combining PI and Self-tuning Regulator. IEEE Trans. Control Syst. Technol.
**2019**, 27, 2663–2671. [Google Scholar] [CrossRef] - Kaicheng, D.; Yan, Z.; Jinjun, L.; Pengxiang, Z.; Jinshui, Z. Dynamic performance improvement of bidirectional switched-capacitor DC/DC converter by right-half-plane zero elimination. In Proceedings of the International Power Electronics Conference (IPEC-Niigata 2018-ECCE Asia), Niigata, Japan, 20–24 May 2018; pp. 4181–4185. [Google Scholar]
- Kesarkar, A.A.; Narayanasamy, S. Asymptotic Magnitude Bode Plots of Fractional-order Transfer Functions. IEEE/CAA J. Autom. Sin.
**2019**, 6, 1019–1026. [Google Scholar] [CrossRef] - Tufenkci, S.; Senol, B.; Alagoz, B.B. Disturbance rejection fractional order PID controller design in V-domain by particle swarm optimization. In Proceedings of the International Artificial Intelligence and Data Processing Symposium (IDAP), Malatya, Turkey, 21–22 September 2019; pp. 1–6. [Google Scholar]
- Nicola, M.; Nicola, C.I. Improved performance of grid-connected photovoltaic system based on fractional-order PI controller and particle swarm optimization. In Proceedings of the 9th International Conference on Modern Power Systems (MPS), Cluj-Napoca, Romania, 16–17 June 2021; pp. 1–5. [Google Scholar]
- Tufenkci, S.; Senol, B.; Alagoz, B.B. Stabilization of fractional order PID controllers for time-delay fractional order plants by using genetic algorithm. In Proceedings of the International Conference on Artificial Intelligence and Data Processing (IDAP), Malatya, Turkey, 28–30 September 2018; pp. 1–6. [Google Scholar]
- Peng, C.C.; Lee, C.L. Performance demands based servo motor speed control: A genetic algorithm proportional-integral control parameters design. In Proceedings of the International Symposium on Computer, Consumer and Control (IS3C), Taichung City, Taiwan, 13–16 November 2020; pp. 469–472. [Google Scholar]
- Wang, Y.; Ying, Z.; Zhang, W. Unified sliding mode control of boost converters with quantitative dynamic and static performances. In Proceedings of the 46th Annual Conference of the IEEE Industrial Electronics Society (IECON 2020), Singapore, 18–21 October 2020; pp. 3271–3276. [Google Scholar]
- Mohanty, S.; Choudhury, A.; Pati, S.; Kar, S.K.; Khatua, S. A comparative analysis between a single loop PI, double loop PI and sliding mode control structure for a buck converter. In Proceedings of the 1st Odisha International Conference on Electrical Power Engineering, Communication and Computing Technology (ODICON), Bhubaneswar, India, 8–9 January 2021; pp. 1–6. [Google Scholar]
- Li, Z.; Yuan, Y.; Wang, H.N. Fuzzy adaptive time-delay feedback controlling chaos in buck converter. In Proceedings of the Chinese Control and Decision Conference (CCDC), Hefei, China, 22–24 August 2020; pp. 4732–4737. [Google Scholar]
- Aarti, D.S.; Arun, N.K. Liquid level control of quadruple conical tank system using linear PI and fuzzy PI controllers. In Proceedings of the 2nd International Conference for Emerging Technology (INCET), Belagavi, India, 21–23 May 2021; pp. 1–5. [Google Scholar]
- Liu, Z.H.; Nie, J.; Wei, H.L.; Chen, L.; Li, X.H.; Lv, M.Y. Switched PI Control Based MRAS for Sensorless Control of PMSM Drives Using Fuzzy-logic-controller. IEEE J. Power Electron.
**2022**, 3, 368–381. [Google Scholar] [CrossRef] - Naung, Y.; Anatolii, S.; Lin, Y.H. Speed control of DC motor by using neural network parameter tuner for PI-controller. In Proceedings of the IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), Saint Petersburg and Moscow, Russia, 28–31 January 2019; pp. 2152–2156. [Google Scholar]
- Chao, K.H.; Huang, C.H. Bidirectional DC-DC Soft-switching Converter for Stand-alone Photovoltaic Power Generation Systems. IET Power Electron.
**2014**, 7, 1557–1565. [Google Scholar] [CrossRef] - Jian, J.J. Energy Storage System with Uniform Battery Charging and Discharging Control. Master’s Thesis, National Chin-Yi University of Technology, Taichung City, Taiwan, 23 July 2020. [Google Scholar]
- Ram, J.P.; Pillai, D.S.; Rajasekar, N.; Strachan, S.M. Detection and Identification of Global Maximum Power Point Operation in Solar PV Applications Using a Hybrid ELPSO-P&O Tracking Technique. IEEE Trans. Emerg. Sel. Topics Power Electron.
**2020**, 8, 1361–1374. [Google Scholar] - Tang, C.Y.; Wu, H.J.; Liao, C.Y.; Wu, H.H. An Optimal Frequency-modulated Hybrid MPPT Algorithm for the LLC Resonant Converter in PV Power Applications. IEEE Trans. Power Electron.
**2022**, 37, 944–954. [Google Scholar] [CrossRef] - TMS320F2809 Data Manual, Texas Instruments. October 2003. Available online: https://www.ti.com/lit/ds/symlink/tms320f2809.pdf?ts=1594465026502&ref_url=https%253A%252F%252Fwww.ti.com%252Fprodu107ct%252FTMS320F2809.pdf (accessed on 23 August 2022).
- Gao, Z.H.; Xie, H.C.; Yang, X.B.; Niu, W.F.; Li, S.; Chen, S.Y. The Dilemma of C-Rate and Cycle Life for Lithium-Ion Batteries under Low Temperature Fast Charging. Batteries
**2022**, 8, 234. [Google Scholar] [CrossRef] - Chen, P.Y.; Chao, K.H.; Chen, H.J. Modeling and Quantitative Design of a Controller for a Bidirectional Converter with High Voltage Conversion Ratio. Int. J. Innov. Comput. Inf. Control
**2018**, 14, 2203–2219. [Google Scholar] - R&S
^{®}NGL200/NGM200 Power Supply Series User Manual. Available online: https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/pdm/cl_manuals/user_manual/1178_8736_01/NGL200_NGM200_UserManual_en_10.pdf. (accessed on 23 August 2022).

**Figure 1.**Architecture of the PMA combined with the energy storage battery system with equalizing charge/discharge control.

**Figure 3.**The adopted equalizing charge/discharge circuit architecture [1].

**Figure 4.**The equivalent circuit of the bidirectional buck–boost converter when the low-voltage side switch S

_{L}is conducting and the high-voltage side switch S

_{H}is in a cut-off state.

**Figure 5.**The equivalent circuit of the bidirectional buck–boost converter when the low-voltage side switch S

_{L}is in a cut-off state and the high-voltage side switch S

_{H}is conducting.

**Figure 6.**Block diagram of control system for input current of the bidirectional soft-switching converter.

**Figure 7.**Bode plot of the current loop frequency response for the ${K}_{Ii}=\mathrm{10,000}$ under different K

_{Pi}.

**Figure 9.**Output voltage response waveform of changing to 240 V from 180 V by the DC-link voltage step command.

**Figure 10.**Output voltage response waveform as P

_{pv}drops from 1000 W to 900 W due to variation in sunlight.

**Figure 12.**Physical circuit for the PMA combined with the battery equalizing charge/discharge control.

**Figure 13.**Experiment operating environment for the PVMA combined with the battery equalizing charge/discharge control.

**Figure 14.**DC-link voltage response waveform of the quantitatively designed controller: (

**a**) sunlight drops to 900 W/m

^{2}from 1000 W/m

^{2}; (

**b**) sunlight increases to 1000 W/m

^{2}from 900 W/m

^{2}.

**Figure 15.**DC-link voltage response waveform of the traditional P-I controller obtained by the trial-and-error method: (

**a**) sunlight drops to 900 W/m

^{2}from 1000 W/m

^{2}; (

**b**) sunlight increases to 1000 W/m

^{2}from 900 W/m

^{2}.

**Figure 17.**Equalizing discharge control response of the quantitatively designed controller when V

_{Bat1}= 12.32 V and V

_{Bat2}= 13.12 V: (

**a**) initiate equalizing discharge control; (

**b**) reach equalizing discharge equalization.

**Figure 18.**Equalizing discharge control response of the traditional P-I controller when V

_{Bat1}= 12.32 V and V

_{Bat2}= 13.12 V: (

**a**) initiate equalizing discharge control; (

**b**) reach equalizing discharge equalization.

**Figure 19.**Equalizing discharge control response of the quantitatively designed controller when V

_{Bat1}= 13.29 V and V

_{Bat2}= 12.44 V: (

**a**) initiate equalizing discharge control; (

**b**) reach equalizing discharge equalization.

**Figure 20.**Equalizing discharge control response of the traditional P-I controller when V

_{Bat1}= 13.29 V and V

_{Bat2}= 12.44 V: (

**a**) initiate equalizing discharge control; (

**b**) reach equalizing discharge equalization.

**Figure 22.**Equalizing charge control response of the quantitatively designed controller when V

_{Bat1}= 11.58 V and V

_{Bat2}= 12.65 V: (

**a**) initiate equalizing charge control; (

**b**) reach equalizing charge equalization.

**Figure 23.**Equalizing charge control response of the traditional P-I controller when V

_{Bat1}= 11.58 V and V

_{Bat2}= 12.65 V: (

**a**) initiate equalizing charge control; (

**b**) reach equalizing charge equalization.

**Figure 24.**Equalizing charge control response of the quantitatively designed controller when V

_{Bat1}= 12.85 V and V

_{Bat2}= 11.92 V: (

**a**) initiate equalizing charge control; (

**b**) reach equalizing charge equalization.

**Figure 25.**Equalizing charge control response of the traditional P-I controller when V

_{Bat1}= 12.85 V and V

_{Bat2}= 11.92 V: (

**a**) initiate equalizing charge control; (

**b**) reach equalizing charge equalization.

Parameters | Specifications |
---|---|

Voltage at high-voltage side(V_{Bus}) | 240 V |

Voltage of first battery set at low-voltage side (V_{Bat}_{1}) | 12 V |

Voltage of second battery set at low-voltage side (V_{Bat}_{2}) | 12 V |

Switching frequency (f) | 25 kHz |

Maximum operating power (P_{max}) | 300 W |

Voltage ripple at high-voltage side (ΔV_{Bus,ripple}) | 0.5% |

Voltage ripple at low-voltage side (ΔV_{Bat,ripple}) | 0.5% |

Component Name | Specifications |
---|---|

Main inductor (L_{1}, L_{2}) | 1.425 mH |

Resonance inductor (L_{a}_{1}, L_{a}_{2}) | 18 μH |

Capacitor at high-/low-voltage side (C_{Bat}_{1}, C_{Bat}_{2}, C_{Bus}_{1}, C_{Bus}_{2}) | 270 μF/450 V |

Main switch and auxiliary switch | IGBT-IXGH48N60C3D1 (600 V/48 A) |

**Table 3.**Initial voltage and final voltage after reaching equalizing charge/discharge of each battery set under different PVMA output power.

Operating Mode | Voltage Status | |||
---|---|---|---|---|

Initial Voltage of First Set | Final Equalizing Charge/Discharge Voltage | Initial Voltage of Second Set | Final Equalizing Charge/Discharge Voltage | |

Discharging | V_{Bat}_{1} = 12.32 V | V_{discharge} = 12.15 V (PV power = 200 W) | V_{Bat}_{1} = 13.29 V | V_{discharge} = 12.23 V (PV power = 200 W) |

V_{Bat}_{2} = 13.12 V | V_{Bat}_{2} = 12.44 V | |||

Charging | V_{Bat}_{1} = 11.58 V | V_{charge} = 13.53 V (PV power = 400 W) | V_{Bat}_{1} = 12.85 V | V_{charge} = 13.8 V (PV power = 400 W) |

V_{Bat}_{2} = 12.65 V | V_{Bat}_{2} = 11.92 V |

**Table 4.**Comparison of equalizing discharge time between the quantitatively designed controller and traditional P-I controller.

Controller Used | Battery Status | |
---|---|---|

V_{Bat}_{1} = 12.32 VV _{Bat}_{2} = 13.12 V | V_{Bat}_{1} = 13.29 VV _{Bat}_{2} = 12.44 V | |

Quantitatively designed controller | 33 m 54 s | 34 m 55 s |

Traditional P-I controller | 38 m 28 s | 39 m 05 s |

**Table 5.**Comparison of equalizing charge time between the quantitatively designed controller and traditional P-I controller.

Controller Used | Battery Status | |
---|---|---|

V_{Bat}_{1} = 11.58 VV _{Bat}_{2} = 12.65 V | V_{Bat}_{1} = 12.85 VV _{Bat}_{2} = 11.92 V | |

Quantitatively designed controller | 42 m 31 s | 41 m 40 s |

Traditional P-I controller | 46 m 40 s | 46 m 04 s |

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## Share and Cite

**MDPI and ACS Style**

Chao, K.-H.; Huang, B.-Z.
Quantitative Design for the Battery Equalizing Charge/Discharge Controller of the Photovoltaic Energy Storage System. *Batteries* **2022**, *8*, 278.
https://doi.org/10.3390/batteries8120278

**AMA Style**

Chao K-H, Huang B-Z.
Quantitative Design for the Battery Equalizing Charge/Discharge Controller of the Photovoltaic Energy Storage System. *Batteries*. 2022; 8(12):278.
https://doi.org/10.3390/batteries8120278

**Chicago/Turabian Style**

Chao, Kuei-Hsiang, and Bing-Ze Huang.
2022. "Quantitative Design for the Battery Equalizing Charge/Discharge Controller of the Photovoltaic Energy Storage System" *Batteries* 8, no. 12: 278.
https://doi.org/10.3390/batteries8120278