# A Grid Connected Photovoltaic Inverter with Battery-Supercapacitor Hybrid Energy Storage

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Present State of the Art

#### 1.2. Literature Review

- Microgrids are the most used application for high power including energy management through global control with connection to grid when there is no energy stored. Some other applications are power injection regulation for tracking the forecasts, smoothing the fluctuating output power of the PV plant and power sharing.
- The trend when using ESS is to implement independent power stages for each power source, which means a boost stage for photovoltaics [30]. Photovoltaic inverters with two or more stages are usually implemented in the low-medium power range in order to boost the PV array voltage [31,32]. For higher power ranges, the boost stage is avoided as the PV arrays provide enough voltage and the efficiency is higher [33]. However, the energy management advantages introduced by an ESS require independent stages for each energy source in order to be optimized [34].
- Also, the control scheme is more flexible and robust when each decoupled stage introduces its degrees of freedom, to include all the electrical functions the converter is supposed to have. That is why most of the topologies include boost and DC/DC stages, including high power oriented ones, despite being worse. In addition, the efficiency of the boost stages could be optimized for the design [35].
- The main goal is usually to maintain the battery health, in addition to the particular application purpose. This is done using the supercapacitor for the sharp changes and developing control strategies that decrease the charge/discharge current rates of battery while maintaining a healthy state of charge (SOC) for both. These techniques also imply reduced current stress levels, less temperature and improved battery life span. Usually, the hybrid solution is done by using a low pass filter (LPF) which provides a high frequency reference for the supercapacitor and a low frequency reference for the battery.

#### 1.3. Motivation and Objective

#### 1.4. Innovative Contribution

## 2. Topology

## 3. Materials and Methods

_{P}travels through the ferromagnetic core and creates a magnetic flux, which is balanced by the magnetic flux created by the secondary current. An electronic stage is implemented in order to improve the accuracy of the primary current waveform representation by compensating the secondary current. By using this configuration, the bandwidth is extended and the time response is reduced.

_{1}. As the primary current will be quite small, a large internal primary coil with many turns is added with the aim of generate the proper primary magnetic flux. Except of that, the voltage transducer follows the same principle of operation the current transducer follows.

_{M}for measuring a voltage drop that is proportional to the primary magnitude.

## 4. HESS Sizing

_{Ch}is the energy charge in the ESS, p

_{S}is the grid injected power in kW, p

_{PV}is the photovoltaic generation power in kW, T

_{s}is sampling time in seconds, i is the sample pointer, m is the time management interval pointer, k is the cumulative pointer, N is the number of samples inside a management time interval and M is the number of management time intervals. Figure 6 shows the PV power generation, the PV power injected into the grid (constant in every 15 min interval and calculated as the average of the next management time interval) and the energy that must be stored. From this, it is possible to determine the minimum ESS size needed on a sunny and a cloudy day. Note that the asymmetry in the sunny day could be due to morning mist. The nominal sunny day generates 28 kW peak which implies a need for a minimum ESS of 0.2 kWh. However, the cloudy day has sharp changes and the ESS needed is close to 1.2 kWh.

_{PV,nom}is the nominal photovoltaic generation power in kW and T

_{m}is the management time interval in s. Considering a nominal PV power of 30 kW, the maximum ESS is 7.5 kWh.

_{Ca}is the ESS capacity decided for the design. The value for the $\raisebox{1ex}{$\tau $}\!\left/ \!\raisebox{-1ex}{${T}_{m}$}\right.$ ratio should be big enough in order to avoid sharp energy changes in the battery, which must be managed by the supercapacitor. Obviously, the compromise is located when the supercapacitor storage system becomes too expensive in the economic study of the converter. Considering the 15-min management time interval and the 7.5 kWh capacity of the ESS, a 0.1 index is a good balance as it implies the supercapacitor supports the battery for more than a minute assuring low battery stress [7] and the cost of the system is affordable [4].

## 5. Control Logic

- The converter enters standby mode when the PV array has low irradiance, which could be evaluated via the PV voltage considering MPPT operation, and the management time interval starts.
- In normal operation mode, every parameter of the converter is working inside the good operating range, and subsequently, the power injected into the grid is the reference power in the interval. This mode is reached from standby when the irradiance is enough, and from the other states when the ESS recovers a good SOC range.
- The battery SOC has reached the top allowed level or the battery charging current becomes saturated. This means the PV generation is too high. In order to maintain the injected power reference, the system sets the reference power point tracking (RPPT) instead of the MPPT by saturating the PV boost current, i
_{PV,sat}. In case of high battery SOC, the RPPT is obtained for zero battery power flow and at the end of the management time interval, the PV boost stage operates on MPPT for the next p_{s,ref}calculation in an optimistic way in order to force battery discharge. If the battery current is saturated, the RPPT is obtained to avoid current battery saturation. - Battery SOC is at the minimum value or battery current is saturated at its maximum value. This is a critical state, where p
_{s,ref}must change before the end of the management time interval for zero or non-saturated battery power flow because of low PV irradiance. p_{S,ref}is calculated in a pessimistic way for the next cycle. - Supercapacitor has reached its top voltage. Negative power flow for the supercapacitor by adding a steady state negative offset, i
_{SC,offset}. - Supercapacitor voltage is too low. Positive power flow for the supercapacitor by adding a steady state positive offset.

_{PV,sat}depending on the state. Then a PI controller tracks it by acting over the PV boost duty cycle.

_{abc}, and currents, i

_{abc}, are transformed into the dq voltages, v

_{dq}, and currents, i

_{dq}, components for and easier current control [38]. The Phase Locked Loop (PLL) synchronizes with the fundamental positive sequence component of the grid voltage [39]. The d current reference is directly obtained by the grid power reference generated in the state machine. The q current reference is set to zero for null grid reactive power injection. Inverter reference voltages are obtained in the dq frame by using a feed forward scheme, which decouples d and q terms:

## 6. Simulation

^{−6}s while the simulation step for the control algorithm was set to the sample rate the measurements are acquired (2 × 10

^{−4}s). In this way, the simulation could be compared with the real behavior, as the power electronics are simulated with great detail and the control algorithm updates when the control board does.

## 7. Experimental Results

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Acronyms

AC | Alternating Current |

B | Battery |

CAES | Compressed Air Energy Storage |

DC | Direct Current |

DER | Distributed Energy Resource |

dq | Direct-quadrature |

ESS | Energy Storage Systems |

HESS | Hybrid Energy Storage Systems |

LPF | Low Pass Filter |

MPPT | Maximum Power Point Tracking |

PHS | Pumped Hydropower Storage |

PI | Proportional Integral |

PLL | Phase Locked Loop |

PV | PhotoVoltaic |

PWM | Pulse Width Modulation |

RPPT | Reference Power Point Tracking |

SC | SuperCapacitors |

SOC | State Of Charge |

THD | Total Harmonic Distortion |

UPS | Uninterruptible Power Supply |

## Nomenclature

$a$, $b$, $c$ | Grid phases |

${C}_{I,a}$; ${C}_{I,b}$; ${C}_{I,c}$ | Inverter output filter capacitors |

${C}_{1}$, ${C}_{2}$ | DC link capacitors |

${C}_{PV}$ | PV boost stage capacitor |

${D}_{B}$ | DC/DC battery converter duty cycle |

${D}_{PV}$ | Boost converter duty cycle |

${D}_{SC}$ | DC/DC supercapacitor converter duty cycle |

$ES{S}_{Ca,B}$ | Battery ESS capacity |

$ES{S}_{Ca,max}$ | Maximum ESS capacity needed for a certain design |

$ES{S}_{Ca,min}$ | Minimum ESS capacity required for a certain design |

$ES{S}_{Ca,SC}$ | Supercapacitor ESS capacity |

$ES{S}_{Ca}$ | Full ESS capacity |

$ES{S}_{Ch}$ | Energy charge in the ESS |

$i$ | sample pointer |

${i}_{d,ref}$ | Grid direct reference current |

${i}_{I,a}$; ${i}_{I,b}$; ${i}_{I,c}$ | Inverter output currents |

${i}_{PV,sat}$ | PV current saturation for RPPT |

${i}_{q,ref}$ | Grid quadrature reference current |

${i}_{S,a}$; ${i}_{S,b}$; ${i}_{S,c}$ | Grid currents |

${i}_{SC,offset}$ | Offset current term for the supercapacitor converter |

${i}_{B}$ | Battery current |

${i}_{dq}$ | Grid dq current |

${i}_{PV}$, | PV module current |

${i}_{SC}$ | Supercapacitor converter current |

$k$ | cumulative pointer |

$L$ | Equivalent grid filter indtor |

${L}_{I,a}$; ${L}_{I,b}$; ${L}_{I,c}$ | Inverter output filter inductances (inverter side) |

${L}_{S,a}$; ${L}_{S,b}$; ${L}_{S,c}$ | Inverter output filter inductances (grid side) |

${L}_{B}$ | DC/DC battery converter inductance |

${L}_{PV}$ | Boost converter inductance |

${L}_{S}$ | Inverter output filter inductances (grid side) |

${L}_{SC}$ | DC/DC supercapacitor converter inductance |

$M$ | number of management time intervals |

$m$ | time management interval pointer |

${m}_{abc}$ | Inverter duty cycle |

$N$ | number of samples inside a management time interval |

$o$ | Middle point of the DC link |

${p}_{PV,nom}$ | Nminal power of the converter |

${p}_{s,\mathrm{ref}}$ | Reference active power set-point |

${p}_{B}$ | Battery power |

${p}_{PV}$ | Photovoltaic generation power |

${p}_{PV}$ | PV module power |

${p}_{S}$ | Grid injected power |

${p}_{SC}$ | Super-capacitor power |

$R$ | Equivalent grid filter resistance |

${R}_{M}$ | External measurement resistance for LEM transducers |

${S}_{a}^{+}$; ${S}_{b}^{+}$; ${S}_{c}^{+}$; ${S}_{a}^{-}$; ${S}_{b}^{-}$; ${S}_{c}^{-}$ | Inverter switching signals |

${S}_{d}$ | Boost converter switching signal |

${S}_{e}^{+}$; ${S}_{e}^{-}$ | DC/DC battery converter switching signals |

${S}_{f}^{+}$; ${S}_{f}^{-}$ | DC/DC supercapacitor converter switching signals |

${T}_{m}$ | Management time interval |

${T}_{s}$ | Sampling time |

${v}_{d,ref}$ | Grid direct reference voltage |

${v}_{DC,\mathrm{ref}}$ | DC link voltage reference value |

${v}_{I,a}$; ${v}_{I,b};\text{}{v}_{I,c}$ | Inverter output voltages |

${v}_{q,ref}$ | Grid quadrature reference voltage |

${v}_{S,a}$; ${v}_{S,b};\text{}{v}_{S,c}$ | Grid Voltages |

${v}_{B}$ | Battery voltage |

${v}_{d}$ | Grid direct voltage |

${v}_{DC}$ | DC link voltage |

${v}_{dq}$ | Grid dq voltages |

${v}_{PV}$ | PV module voltage |

${v}_{q}$ | Grid quadrature voltage |

${v}_{SC}$ | Supercapacitor voltage |

$\tau $ | Low-pass filter time constant |

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**Figure 3.**Picture of the prototype ((1) HP E4351B Solar Array Simulator, (2) Boost converter filter, (3) two Fuji IGBT-IPM 6MBP50RA120 power stage, (4) Li-ion batteries, (5) Maxwell BMOD0165 P048 B01 supercapacitor, (6) ESS converters filters, (7) inverter filter, (8) HP 6834B Power Source/Analyzer, (9) STM32F407 microcontroller based control board, (10) LV 25-P voltage sensors, (11) LA 55P/SP1 current sensors).

**Figure 4.**Hall effect transducers schematic: (

**a**) LA 55P/SP1 current transducer; (

**b**) LV 25-P voltage transducer.

**Figure 5.**Sensors printed circuit boards for the experimental setup for measuring current and voltage magnitudes: (

**a**) current sensors board and (

**b**) voltage sensor board.

**Figure 6.**PV power generation, PV power injected into the grid (calculated as an average of the next 15 min interval forecast) and the energy stored: (

**a**) for a sunny day and (

**b**) for a cloudy day.

**Figure 7.**PV power generation, PV power injected into the grid (obtained from the PV power generation at the end of the previous 15-min interval) and the energy stored: (

**a**) for a sunny day and (

**b**) for a cloudy day.

**Figure 8.**Control logic: (

**a**) full scheme, (

**b**) state machine, (

**c**) MPPT, (

**d**) HESS diagram and (

**e**) dq diagram.

**Figure 9.**Simulation results. (

**a**) Irradiance, PV output voltage; PV output current, PV output power and DC link voltage, (

**b**) Voltage and current in the dq frame and power injected into the grid and (

**c**) Grid voltage, inverter currents and grid currents.

**Figure 10.**Simulation results: (

**a**) Battery magnitudes and (

**b**) supercapacitor magnitudes and HESS power.

**Figure 11.**Experimental results. (

**a**) PV current, grid current, battery and supercapacitor current for a cyclic injected power reference operation. (

**b**) Grid voltage, grid current, battery and supercapacitor current for steady state operation.

Paper | [9] | [10] | [11] | [12] | [13] | [14] | [15] | [16] | [17] |
---|---|---|---|---|---|---|---|---|---|

Application | Pulse-operated power systems | Load supply | Energy harvesting | Load supply | Load supply | Load supply | Load supply | Load supply | Load supply |

System | DC | DC | DC | DC | DC | DC + 3~Alternating Current (AC) | DC | DC | DC |

Topology | Active Hybrid Bidirectional DCDC | Bidirectional DCDC | PV Boost + Bidirectional DCDC | Bidirectional DCDC | PV Boost Bidirectional DCDC | PV Boost + Bidirectional DCDC + 3~Inverter | PV Boost + Bidirectional DCDC | Bidirectional DCDC | PV Boost + Bidirectional DCDC |

Rated Power | 132 W | 500 W | 5 W | 50 W | 100 W | 1 kW | 50 W | 100 W | 2 kW |

Comparison | Passive vs. Active hybrid | Napoli vs. MIAD | - | - | - | LPF vs. Haar wavelet vs. Fuzzy | - | - | ESS vs. HESS |

Sizing | - | - | Statistical analysis | - | - | - | Optimization flowchart | - | - |

Control | Proportional Integral (PI) | Multiplicative-increase-additive-decrease (MIAD) | State machine | Predictive control | PI with LPF | Multimode fuzzy-logic power allocator | - | state-space averaged model | Flatness approach |

Goals | More power Lower battery temperature Longer battery lifetime | Minimization of the battery current fluctuation and SC energy loss | Increase battery lifetime | Battery current and state of charge SC into the limits | Improve the life span and reduce the current stresses on battery | Avoid depleting or saturating the two components Relaxing the stress on batteries | Healthy SOC | Control design | Role of SC as a transient power source |

Paper | [18] | [19] | [20] | [21] | [22,23] | [24] | [25] | [26] | [27] |
---|---|---|---|---|---|---|---|---|---|

Application | Microgrids | UPS | Hybrid microgrid | Remote Area Power Supply | Grid-connected photovoltaic | Microgrid | Microgrid | Microgrid | Power sharing |

System | DC | DC | DC + 3~AC | DC + 3~AC | DC + 3~AC | DC + 3~AC | DC + 3~AC | DC + 3~AC | |

Topology | Dual active bridge | Bidirectional DCDC | PV Boost + 3~Inverter and Bidirectional DCDC + 3~Inverter | Wind Rectifier-Boost + Bidirectional DCDC + 3~Inverter | PV Boost + Bidirectional DCDC + 3~Inverter | Bidirectional DCDC + 3~Inverter | PV Boost + 3~Inverter and Bidirectional DCDC + 3~Inverter | PV Boost + Bidirectional DCDC + 3~Inverter | Bidirectional DCDC + 3~Inverter |

Rated Power | 5 kW Modular | 500 kVA | 30 kW | 25 kW | 1 MW | 10 kW | 60 kW | 100 kW | 4 MW |

Comparison | - | - | Different capacities | LPF | - | two-loop PI control and PI sliding mode | - | - | Multi-objective optimization problem (MOP), LPF and LUT |

Sizing | - | Backup time | Power grading | Equations | SC as 1/5 battery | - | Monte Carlo capacity model | - | - |

Control | LPF Energy management | Power sharing | State of charge with load control | Energy management algorithm | Semischeduled generation | Sliding mode | Hysteretic loop | PI controllers and Direct Power Control | Linear weighted summation algorithm |

Goals | Energy balance with renewables | Optimal SC-battery combination vs SC cost | Power balance and ESS in healthy state | Robust voltage and frequency regulation Effective HESS management | Avoid low power level battery operation | Using a nonlinear controller | Extend the battery lifetime by avoiding small cycles | Maintain the grid power demand coming from the grid operator | Optimization of the energy loss and state of charge of the SC |

Current Transducers | Specification | Voltage Transducers |
---|---|---|

0 ... ±100 A | Measuring range | 0 ... ±14 mA (10 mA/500 V) |

25 mA | Secondary nominal current rms | 25 mA |

±12 ... 15 V | Supply voltage | ±15 V (±5%) |

200 kHz | Frequency bandwith | 200 kHz |

2.5 kV rms | Isolation | 2.5 kV rms |

1:2000 | Conversion ratio | 2500:1000 |

±0.9% | Accuracy | ±0.9% |

−40 °C to 85 °C | Operating temperature | 0 °C to 70 °C |

Symbol | Value | Symbol | Value | Symbol | Value |
---|---|---|---|---|---|

p_{PV,nom} | 30 kW | ESS_{Ca,B} | 3 kWh | L_{PV} | 10 mH |

T_{m} | 2 s | ESS_{Ca,SC} | 0.3 kWh | L_{B} = L_{SC} | 20 mH |

τ | 0.2 s | PWM | 5 kHz | LCL | 5 mH, 10 μF, 5 mH |

v_{DC,ref} | 720 V | C_{1}, C_{2} | 2.2 mF | C_{SC} | 37.5 F |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Miñambres-Marcos, V.M.; Guerrero-Martínez, M.Á.; Barrero-González, F.; Milanés-Montero, M.I.
A Grid Connected Photovoltaic Inverter with Battery-Supercapacitor Hybrid Energy Storage. *Sensors* **2017**, *17*, 1856.
https://doi.org/10.3390/s17081856

**AMA Style**

Miñambres-Marcos VM, Guerrero-Martínez MÁ, Barrero-González F, Milanés-Montero MI.
A Grid Connected Photovoltaic Inverter with Battery-Supercapacitor Hybrid Energy Storage. *Sensors*. 2017; 17(8):1856.
https://doi.org/10.3390/s17081856

**Chicago/Turabian Style**

Miñambres-Marcos, Víctor Manuel, Miguel Ángel Guerrero-Martínez, Fermín Barrero-González, and María Isabel Milanés-Montero.
2017. "A Grid Connected Photovoltaic Inverter with Battery-Supercapacitor Hybrid Energy Storage" *Sensors* 17, no. 8: 1856.
https://doi.org/10.3390/s17081856