# Optimal Energy Management Scheme of Battery Supercapacitor-Based Bidirectional Converter for DC Microgrid Applications

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## Abstract

**:**

## 1. Introduction

_{SC}within predefined limits, rendering SC protection difficult.

- ▪
- This research work proposes a DC Microgrid voltage stabilization based on multi-input converters.
- ▪
- A comprehensive controller is introduced for the design and analysis of a HESS-based multiple-input bidirectional converter. For a multi-input converter, the small-signal model-based-provided controller ensures stability in all working areas.
- ▪
- The execution of an energy management system for a multiple-input bi-directional converter with HESS is introduced for different PV and load conditions. The EMS can undoubtedly follow the SC SoC and empower various modes to guarantee safe activity.
- ▪
- The primary benefit of the planned double-input bidirectional converter is its energy trade mode, which permits charging the SC freely from the battery. The double-input bidirectional converter has many advantages, including compelling power assignment between the different ESSs, quicker DC link voltage regulation, etc. PV power fluctuations and load disturbances require faster DC link voltage management.
- ▪
- The proposed modified converter operation allowed for the use of a similar controller for both HESS charging and discharging operations, resulting in a unified controller.
- ▪
- The DC grid voltage profile can be significantly improved in terms of settling time and maximum peak overshoot when using the predictive PI control compared to the proposed and traditional PI control methods.

## 2. Operation of a Bidirectional DC-DC Converter with Dual Inputs

_{B}) and supercapacitor voltage (V

_{S}) modules, respectively, while Leg 1 is connected to a DC Microgrid voltage (V

_{DC}). In this converter topology, the voltage across the battery is lower than the DC grid voltage but higher than the supercapacitor voltage. The inductors L

_{B}and L

_{S}with High-frequency connect legs 1, 2, and 3 together. The following sections describe the various modes of operation.

#### 2.1. Discharging Sequence of HESS

_{1}/S

_{2}, S

_{3}/S

_{4}, and S

_{5}/S

_{6}are all switch pairs that work in tandem. In this mode, the switch pairs S

_{2}/S

_{5}and S

_{1}/S

_{6}always switch together, with complementary gating pulses. Switches S

_{2}, S

_{3}, and S

_{5}are turned on at time instant t

_{0}, causing inductor currents i

_{B}and i

_{S}to grow linearly with slopes V

_{B}/L

_{B}and V

_{S}/L

_{S}, respectively. At t

_{1}, switch S

_{3}is turned off, allowing current i

_{B}to flow freely through the S

_{4}body diode. Switch S

_{4}is turned on after a dead time interval for the switch pair S

_{3}/S

_{4}. S

_{4}comes on with ZVS because its body diode is already conducting at the time the gating signal is sent. At t

_{2}, switches S

_{2}and S

_{5}are disabled, forcing inductor current i

_{L2}to flow through the body diodes of switches S

_{1}and S

_{6}with a negative V

_{DC}/L

_{S}slope. With a negative slope of V

_{DC}/L

_{B}, inductor current i

_{B}flows via S

_{1}body diode. Switch pairs S

_{2}/S

_{1}and S

_{5}/S

_{6}are gated on after the dead time intervals of switch pairs S

_{2}/S

_{1}. Because the body diodes of the corresponding switches are already in conduction, switches S

_{1}and S

_{6}are likewise turned on using ZVS, just as S

_{4}. S

_{1}, S

_{4}, and S

_{6}are turned off at t

_{3}.

_{2}, S

_{3}, and S

_{5}will conduct in order to keep the inductor currents flowing. Currents i

_{B}and i

_{S}flow with V

_{B}/L

_{B}and V

_{S}/L

_{S}positive slopes, respectively. Gating pulses are sent to switches S

_{2}, S

_{3}, and S

_{5}, which turn on with ZVS after a dead time gap. Applying a volt-second balance to the inductors L

_{S}and L

_{B}give results when d

_{B}is the duty cycle of the triggering pulse given to switch S

_{3}and d

_{S}is the duty cycle of the triggering pulse delivered to switches S

_{2}and S

_{5}.

_{B}is bigger than ${V}_{S}$. As a result, the flow of power from the battery and supercapacitor to the DC Microgrid can be controlled individually by controlling d

_{B}and ${d}_{S}$.

#### 2.2. Charging Sequence of the HESS

_{1}and S

_{6}switch pairs are switched at the same time. S

_{2}and S

_{5}switch pairs are also gated at the same time, but with pulses that are complementary to S

_{1}and S

_{6}. Switches S

_{4}and S

_{3}are also gated in a complementary manner. At t

_{0}, S

_{1}, S

_{4}, and S

_{6}switches are activated causing the inductor currents i

_{B}and i

_{S}to decrease linearly in a negative direction with slopes V

_{DC}/L

_{B}and V

_{DC}/L

_{S}, respectively.

_{1}, the L

_{B}and L

_{S}inductors store energy during this period. At t

_{1}, the switch pair S

_{1}/S

_{6}was turned off. The body diodes of switches S

_{2}and S

_{5}are turned on to maintain the inductor current i

_{s}. The supercapacitor is now charged using the energy stored in the inductor L

_{S}. Through the body diode of switch S

_{2}, the inductor current i

_{B}freely circulates. Because the body diodes of the corresponding switches are already in conduction after a dead time interval for switch pairs S

_{1}/S

_{6}and S

_{2}/S

_{5}, gating pulses are provided to S

_{2}and S

_{5}, turning them on with ZVS. At time instant t

_{2}

_{,}switch S

_{4}is turned off. Inductor current i

_{S}increases almost linearly with slope V

_{S}/L

_{S}through the body diode of switch S

_{3}. After the switch pair S

_{4}/S

_{3}has reached its dead time interval, a gating pulse is triggered to S

_{3}to turn it on with ZVS. The collected and stored energy in the inductor L

_{B}is now applied to charge the battery. Switches S

_{2}, S

_{3,}and S

_{5}are turned off at instant t

_{3}, causing the body diodes of switches S

_{1}, S

_{4}, and S

_{6}to turn on in order to keep the inductor currents flowing. To turn S

_{1}, S

_{4}, and S

_{6}on with ZVS, triggering pulses are applied after dead time intervals. Applying a volt-second balance equation to the inductors L

_{S}and L

_{B}lead-in, if d

_{S}is the duty cycle of the gating pulse to the S

_{1}/S

_{6}switch pair and d

_{B}is the duty cycle of the triggering pulse to switch S

_{4}.

#### 2.3. HESS Mode of Energy Exchange

_{1}and S

_{2}) is inactive, substantially isolating the DC Microgrid from the HESS while supercapacitor charging. S

_{5}/S

_{6}switch pairs and S

_{3}/S

_{4}switch pairs complement. In this mode, switch S

_{5}is always turned on, causing switch S

_{6}to be turned off. The duty cycle d is applied to switch S

_{3}. Figure 6 depicts the waveforms (b). Switch S

_{3}controls the power stream from the battery to the supercapacitor, with the current ripple greatly decreased by connecting the inductors L

_{B}and L

_{S}in series. The user can adjust the power flow from the battery to the supercapacitor by using the d parameter. When the volt-second balanced equivalent series inductor L (L = L

_{B}+ L

_{S}) is used, the result is:

_{3}allows power to flow from supercapacitor to battery. Switch S

_{4}is in boost mode, as indicated by this action. The procedure is similar to the one described previously.

#### 2.4. Transitions between Modes

_{i}is the supercapacitor’s initial state of charge, Q

_{SC}is the rated charge for the supercapacitor, and i

_{CH}is the charging current of the supercapacitor.

## 3. Double-Input Bidirectional Converter and Controller Design Using a Small Signal Linear Averaged Model

#### 3.1. Design of Conventional and Proposed PI Control Scheme

_{DC}) is compared with a reference voltage (V

_{DC,ref}) and the error is offered to the PI controller in both schemes, which generates total current (i

_{tot}) from ESS in this process. In the conventional control scheme, total current is divided into low-frequency (I

_{LOW}) and high-frequency (I

_{HIGH}) components of current using a low pass filter, which is given as reference currents to battery and supercapacitor loops, respectively, and is represented in Figure 8. In the conventional control scheme, SC current reference consists of a high-frequency component and battery error component which is explained in the proposed control scheme. The conventional control scheme neglects battery current errors arising due to the battery controller.

_{std}), and (ii) transient power component (P

_{tran}). The power balance equation is given as

_{dc}(t) − P

_{ren}(t) = P

_{B}(t) + P

_{SC}(t) = P

_{std}(t) + P

_{tran}(t)

_{dc}(t), P

_{ren}(t), P

_{B}(t) and P

_{SC}(t) are the DC grid power, RES power, battery, and SC power respectively. The HESS charges and discharges, maintaining the DC grid voltage within predefined limits. The sum of battery and SC powers are given as

_{B}(t) + P

_{SC}(t) = P

_{std}(t) + P

_{tran}(t) = V

_{DC}.i

_{tot}(t)

_{p,v}and K

_{i,v}are the proportional and integral constants of the outer voltage control loop, respectively, and v

_{err}represents voltage error. Better DC bus voltage regulation is achieved by effective sharing of total current demand (${i}_{tot}$). In a conventional control scheme, a low pass filter (LPF) extracts the steady-state component from the total current (${i}_{tot}$).

_{B}and d

_{SC}are the duty cycle for battery control and SC control, as shown in Figure 10.

#### 3.1.1. The Supercapacitor-DC Microgrid Stage Small Signal Linear Averaged Model

_{0}~t

_{2}) can be framed as shown in Figure 4 and as discussed in Section 3.

_{2}~t

_{3}), the state equations can be framed as:

#### 3.1.2. Modeling a Battery-DC Microgrid Stage with a Small-Signal Linear Averaged Model

_{0}~t

_{1}) are as follows, as discussed in Section 3.

_{B}, V

_{DC}), U is a matrix consisting of inputs, and Y is a matrix consisting of all the system outputs. It can be rewritten in matrix form as:

_{1}~t

_{2}), in matrix form, the state equations and state model can be framed as follows:

_{2}~t

_{3}), in matrix form, the state equations and state model can be framed as follows:

_{B}∙ T

_{S}), after which it will transition to the model represented by (26), where it will stay for a duration of [(d

_{S}− d

_{B}) ∙ T

_{S}], as shown in Figure 4. For the designed model, the duration of the third time interval is [(1 − d

_{S}) ∙ T

_{S}] (28). As a result, the following is the converter’s averaged state model:

_{B}and d

_{S}) are duty cycles and both inputs are perturbed (u),

_{1}− A

_{2})X + (B

_{1}− B

_{2})U, G = (A

_{2}− A

_{3})X + (B

_{2}− B

_{3})U, and X = −A

^{−1}BU. Applying Laplace transform to (32), the controlled output transfer function of the battery stage is reframed as:

_{1}, C

_{2}, and X from (29), (32), (24), and (26), the current transfer function from battery stage control to the inductor can be configured as follows:

#### 3.2. Predictive PI Control Scheme

#### Inner Predictive PI Control Scheme

## 4. State-of-Charge Controller for Supercapacitors

_{CH}. When the SoC reaches the maximum safe zone, the supercapacitor is allowed to discharge its extra energy to the battery, allowing the battery to operate at a constant current I

_{CH}. As discussed in Section 3, either the buck (SC charging) or boost (SC discharging) operation keeps the supercapacitor’s SoC within acceptable ranges. The SoC controller’s control logic is illustrated in Figure 15. A PI controller regulates the supercapacitor current. The controller’s design is based on the buck mode control-to-output transfer function. It is worth noting that the DC Microgrid is electrically isolated from the HESS whenever the HESS Energy exchange mode is triggered, whether due to high or low SoC values.

## 5. Simulation Results and Analysis

#### 5.1. Step Increase in PV Generation

#### 5.2. Step Decrease in PV Generation

#### 5.3. Step Increase in Load Demand

_{DC}= 48 V, i

_{PV}= 3 A, i

_{o}= 2 A. At t = 0.3 s, the load demand increases to 192 W, which is beyond the power range of PV generation. This creates a power imbalance between source power and load power. The HESS immediately responds, SC supplies the transient component, and the battery supplies the steady-state component of power demand. The DC grid voltage is regulated at 100 ms in the conventional control scheme and 40 ms in the proposed control scheme.

#### 5.4. Step Decrease in Load Demand

#### 5.5. Step Change in PV Generation for Predictive PI Control Scheme

_{P}) settling time (t

_{ss}) of DC Microgrid voltage during a step change in PV generation was examined. The load demand is kept constant in this case, by keeping R

_{dc}= 24 Ω. By changing the PV current control reference, a step change in PV generation is applied to the steady-state system.

_{DC}) is 0.5 V and 2 V, respectively. The corresponding %M

_{P}values are 1.04% and 4.1%, respectively. Step increase and decrease in PV generation have settling times (t

_{ss}) of 2 ms and 5 ms, respectively.

#### 5.6. Step Change in Load Demand

_{DC}) are 3 V and 2.5 V, respectively. The corresponding %M

_{P}values are 6.25% and 5.2%, respectively. Step increases and decreases in load demand, with settling times (t

_{ss}) of 3 ms and 10 ms, respectively.

#### 5.7. Comparative Performance Evaluation

## 6. Experimental Results

#### 6.1. HESS Charging Mode

_{1}. At t

_{1}, the load resistance is increased to 35 Ω and as a result of a decrease in load demand, the excess energy in the dc grid causes a surge in grid voltage. Immediately, the HESS responds in such a manner that the transient component of the current is the charging supercapacitor and the battery charging current is allowed to increase slowly until a steady-state value at instant t

_{2}.

_{3}. The battery and supercapacitor then return to their floating state as it was before t

_{1}. At instants t

_{1}and t

_{3}, DC Microgrid voltage is retained at 20 V almost instantly, as indicated by small spikes in Figure 24a. The battery and supercapacitor SoC are shown in Figure 24b. At instant t

_{1}, SoC

_{SC}is shown to be increasing, indicating charging of the supercapacitor. After the transient current has died out, the supercapacitor remains idle, as indicated by constant SoC. Battery SoC is almost constant, with its energy not depleted quickly compared to the supercapacitor.

#### 6.2. HESS Discharging Mode

_{PV}) of the boost converter connected to RPS while maintaining the input voltage (V

_{PV}) at 12 V.

_{1}, I

_{PV}is decreased from 1.3 A to 1.1 A. This causes DC Microgrid voltage to dip since there exists a power mismatch between source and load. The deficient power is then fed by the HESS by discharging the battery and supercapacitor. Transient current is met by the supercapacitor and steady-state current is supplied by battery, as is evident from current waveforms in Figure 25a. The combined action of battery and supercapacitor maintain DC Microgrid voltage at the nominal value of 20 V. A small spike in voltage waveform is negligible due to the fast dynamics of the HESS. Battery charging current is allowed to increase slowly until a steady-state value at instant t

_{2}.

_{3}, PV generation is reverted back to normal by setting I

_{PV}= 1.3 A. Battery current now slowly reduces to zero whereas the supercapacitor instantly responds to bring DC Microgrid voltage back to nominal value almost instantly. The battery and supercapacitor SoC waveform are also shown in Figure 25b to validate the above-explained operation. When PV generation is decreased at instant t

_{1}, SoC of SC is found to decrease as long as the supercapacitor supplies current indicating discharge operation of the supercapacitor. The supercapacitor is then idle, as indicated by the constant SoC waveform. Similarly, at instant t

_{3}, SoC is increased to indicate charging of the supercapacitor after which it stays idle.

#### 6.3. HESS Energy Exchange Mode

_{1}. Due to reduced PV generation, the grid voltage is now 18 V. At instant t

_{1}, the HESS is active to produce grid voltage at the nominal value of 20 V. Battery and supercapacitor waveforms are as explained in HESS discharging mode. Current waveforms in Figure 26 prove the same result.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## List of Symbols

d_{B} | Battery duty cycle |

d_{SC} | SC duty cycle |

f_{sw} | Switching frequency |

i_{B} | Battery current |

i_{B,ref} | Battery reference current |

i_{SC} | SC current |

i_{SC,ref} | SC reference current |

V_{DC} | DC Microgrid voltage |

V_{DC,ref} | DC grid reference voltage |

V_{B} | Battery voltage |

V_{sc} | Supercapacitor voltage |

L_{B} | Battery inductance |

L_{sc} | Supercapacitor inductance |

SoC_{i} | Supercapacitor’s initial state of charge |

Q_{sc} | Rated charge for Supercapacitor |

i_{tot} | Total current from ESS |

I_{HIGH} | High-frequency component of current |

I_{LOW} | Low-frequency component of current |

P_{std} | Steady-state power component |

P_{tran} | Transient power component |

P_{dc(t)} | DC grid power |

P_{ren(t)} | RES power |

P_{b(t)} | Battery power |

P_{sc(t)} | SC power |

K_{p,v} | Proportional constant of the outer voltage loop |

K_{i,v} | Integral constant of the outer voltage loop |

v_{err} | Voltage error |

P_{B_un} | Uncompensated power from the battery system |

i_{B,err} | Battery error current |

∆i_{L} | Peak-to-peak inductor current |

G_{isc dSC} | Control-to-SC current transfer function |

G_{VDCiSC} | SC current-to-output voltage transfer function |

G_{pi}__{iS} | PI controller transfer function of inner SC current loop |

G_{pi_v} | PI controller transfer function of the outer voltage control loop |

G_{iBdB} | Control-to-battery current transfer function |

G_{pi_iB} | PI controller transfer function of battery current loop |

I_{dc(k)} | Total load current |

V_{dc(k)} | Present sampling DC Microgrid voltage |

V_{sc(k)} | Present sampling SC voltage |

I_{sc(k)} | Present sampling SC current |

V_{B(k)} | Present sampling battery voltage |

i_{B(k)} | Present sampling battery current |

i_{B(k+1)} | Prediction of battery current |

I_{sc(k+1)} | Prediction of SC current |

i_{C} | Charging current |

$\frac{d{v}_{dc}}{dt}$ | Rate of change of DC grid voltage |

T_{s} | Sampling period |

$\frac{d{i}_{b}}{dt}$ | Rate of change of battery current |

$\frac{d{i}_{SC}}{dt}$ | Rate of change of SC current |

d_{b(i)} | Iteratively calculated battery duty cycle |

d_{Sc(i)} | Iteratively calculated SC duty cycle |

J | Objective function of MPC |

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**Figure 1.**Various configurations of a HESS consisting of a battery connected to a DC Microgrid and an SC. (

**a**) Two segregated bidirectional converter modules. (

**b**) Bidirectional converter with single double-input.

**Figure 6.**HESS mode of energy exchange. (

**a**) Current flows across an active circuit. (

**b**) Waveforms in a steady state.

**Figure 8.**Overall management mechanism for current bifurcation between SC and battery units for conventional PI.

**Figure 9.**Overall management mechanism for current bifurcation between SC and battery units for proposed PI.

**Figure 10.**Logic for controlling a supercapacitor and a battery. (

**a**) The supercapacitor control scheme. (

**b**) Battery control system scheme.

**Figure 11.**Bode plot of SC’s inner current controller of logic for control, both with and without controller.

**Figure 12.**Bode plot of SC’s outer voltage controller of logic for control, both with and without controller.

**Figure 15.**Supercapacitor SoC charge controller. (

**a**) Charging and discharging logic; logic for the charging and discharging process. (

**b**) Flowchart of the control logic.

**Figure 22.**Comparative analysis of conventional PI, proposed PI, and predictive PI control schemes. (

**a**,

**b**) DC grid voltage for step change in PV and load, (

**c**) battery current, (

**d**) SC current.

S. No | Specification Parameters | Value |
---|---|---|

1 | Voltage at MPPT(V_{mppt}) | 32 V |

2 | Current of MPPT (I_{mppt}) | 2 A |

3 | Power at MPPT (P_{mppt}) | 96 W |

3 | Supercapacitor voltage (V_{SC}) | 32 V |

4 | Supercapacitor inductance (L_{S}) | 0.355 mH |

5 | Battery voltage (V_{B}) | 24 V |

6 | Inductance in Battery (L_{B}) | 0.3 mH |

7 | Inductance in Boost converter (L) | 4.1 mH |

8 | Resistance (R) in the Converter | 4.8 Ω |

9 | Voltage in DC Microgrid (V_{DC}) | 48 V |

10 | Capacitance (C) | 300 µF |

Conventional PI | Proposed PI | Predictive PI | ||||
---|---|---|---|---|---|---|

Settling Time (t _{ss}) | %MP | Settling Time (t _{ss}) | %MP | Settling Time (t _{ss}) | %MP | |

Step increase in PV generation | 100 ms | 22.9% | 35 ms | 14.58% | 2 ms | 0.01% |

Step decrease in PV generation | 120 ms | 27% | 30 ms | 14.5% | 5 ms | 4.1% |

Step increase in load demand | 100 ms | 25% | 40 ms | 12.5% | 3 ms | 6.25% |

Step decrease in load demand | 80 ms | 29.16% | 30 ms | 16.6% | 10 ms | 5.2% |

S. No | Parameters | Value |
---|---|---|

1 | SC voltage (V_{SC}) | 10 V |

2 | SC inductance (L_{S}) | 1.43 mH |

3 | Battery voltage (V_{B}) | 12 V |

4 | Battery inductance (L_{B}) | 4.8 mH |

5 | Boost inductance (L) | 4.1 mH |

6 | Resistance (R) | 25 Ω |

7 | DC Microgrid voltage (V_{DC}) | 20 V |

8 | Capacitance (C) | 150 µF |

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## Share and Cite

**MDPI and ACS Style**

Punna, S.; Banka, S.; Salkuti, S.R.
Optimal Energy Management Scheme of Battery Supercapacitor-Based Bidirectional Converter for DC Microgrid Applications. *Information* **2022**, *13*, 350.
https://doi.org/10.3390/info13070350

**AMA Style**

Punna S, Banka S, Salkuti SR.
Optimal Energy Management Scheme of Battery Supercapacitor-Based Bidirectional Converter for DC Microgrid Applications. *Information*. 2022; 13(7):350.
https://doi.org/10.3390/info13070350

**Chicago/Turabian Style**

Punna, Srinivas, Sujatha Banka, and Surender Reddy Salkuti.
2022. "Optimal Energy Management Scheme of Battery Supercapacitor-Based Bidirectional Converter for DC Microgrid Applications" *Information* 13, no. 7: 350.
https://doi.org/10.3390/info13070350