# Fuzzy Hysteresis Current Controller for Power Quality Enhancement in Renewable Energy Integrated Clusters

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## Abstract

**:**

^{®}. The performance analysis of the proposed and conventional inverter configurations is done by computing various power quality indices, namely voltage characteristics (swell, sag, and imbalance), frequency characteristics (deviations), and total harmonic distortion. The results reveal that the proposed FHCC-based inverter achieves a better quality of power than the traditional ST-PWM-based multilevel inverter in terms of IEEE/IEC/EN global standards for renewable energy integrated cluster microgrids application.

## 1. Introduction

- ▪
- Proposes the idea of interoperating many adjacent microgrids in an urban energy community to form a renewable-energy-based microgrid cluster. This increases the energy availability, thereby improving the power supply reliability by allowing the cluster to manage its own energy requirement rather than relying on the utility grid;
- ▪
- Proposes a new inverter control mechanism, namely “Fuzzy Hysteresis Current Controller-based Pulse Width Modulation (FHCC-PWM)”, which improves the power supply quality. The proposed fuzzy logic improves the control loop ability to regulate the system under variety of operating conditions.

## 2. Description of the Components Present in Cluster Microgrids

#### 2.1. Description of ST-PWM Based Multilevel Inverter

#### 2.2. Description of Proposed FHCC Based Inverter

#### 2.3. Description of Energy Management Control Unit (EMCU)

#### 2.4. Performance Issues and Measures

- ▪
- Voltage sag/swell: Root mean square (RMS) value of voltage (${V}_{RMS}^{x}$) is calculated by squaring all the sampled voltages and is averaged over a window with a duration of one cycle at the sampling instant x given in Equation (1). Voltage sag and swell are the drop and rise that are observed in the RMS value of the voltage that occurs due to sudden rise and fall of the load, respectively.
- ▪
- Voltage imbalance: It is defined as the ratio of negative sequence voltage to positive sequence voltage expressed in terms of the percentage given in Equation (2).
- ▪
- Frequency variations: The load frequency is to be continuously monitored and maintained close to 50 Hz with the penetration of DG sources in microgrids and is given in Equation (3).
- ▪
- Total harmonic distortion (THD): THD is the measure for the level of distortion (harmonic) present in a three-phase power system. It is calculated by measuring the ratio between the amplitudes (RMS value) of a set of total higher-frequency components with respect to harmonics and the value at fundamental frequency components given in Equations (4) and (5).

_{k}is the recorded voltage waveform sample, ρ is the frequency droop coefficient of cluster microgrids, and $\Delta {P}_{MG}^{i}$ (for I = 1, 2, 3, 4…) is the real power change in the ith microgrid; ${V}_{i}^{rms}$ and ${I}_{i}^{rms}$ are the voltage and current components corresponding to nth harmonic, respectively. Similarly, the voltage and current components with respect to the fundamental frequency of ith microgrid are ${V}_{fund}^{rms}$ and ${I}_{fund}^{rms}$.

## 3. Proposed Fuzzy Hysteresis Current Controller (FHCC)

#### 3.1. Reference (Source) Current Generation

- ▪
- Scheme of fuzzy logic: In this scheme, the fuzzy controller of the proposed inverter is implemented by considering and evaluating some linguistic rules. The internal process of fuzzy controller is explained as follows. The input error value is calculated by taking the difference between the reference voltage (V
^{*}_{dc}) and sensed voltage (V_{dc}). Here, both input signals, i.e., $e(n)$ and $\Delta e(n)$, are numerical variables and are transformed to linguistic variables by considering the following fuzzy sets as given. The characterization of fuzzy logic is as follows:- Consists of seven fuzzy sets (N
_{-3}, N_{-2}, N_{-1}, E_{0}, P_{1}, P_{2}, and P_{3}); - For simplicity, the triangular membership function is considered;
- Mamdani fuzzy inference mechanism is used;
- “Centroid method” is used for defuzzification.

- ▪
- Fuzzification: In this process, instead of numerical values, fuzzy uses linguistic variables. In the system, the error signal can be assigned to negative large (N
_{-3}), negative medium (N_{-2}), negative small (N_{-1}), extreme zero (E_{0}), positive small (P_{1}), positive medium (P_{2}), and positive large (P_{3}). This process converts numerical variables to linguistic variables (fuzzy numbers), and the surface plot of the fuzzy logic controller is shown in Figure 4. - ▪
- Rule elevation: Basic operations of fuzzy logic are needed to evaluate fuzzy set rules shown in Figure 5, which are obtained by considering “union”, “intersection”, and “complement” functions. Considering two fuzzy sets ($\overline{M}$ and $\overline{N}$), the universe $A$ and the following Equations (16)–(18) are the basic relations performed on fuzzy sets.

- ▪
- Process of getting defuzzified output: With the process of defuzzification, a fuzzy set is converted to its crispest version. The mathematical expression for obtaining defuzzified output ${x}^{*}$ is as given in Equation (19).$${x}^{*}=\frac{{\displaystyle \int {\mu}_{\overline{M}}(x)\xb7x\xb7dx}}{{\displaystyle \int {\mu}_{\overline{M}}(x)\xb7x}}$$
- ▪

#### 3.2. Gate Pulses Generation from Hysteresis Current Controller

- (1)
- If ${I}_{act}^{MG,i}(t)<({I}_{ref}^{*MG,i}(t)-{H}_{B})$, then inverter upper switch is OFF, and lower switch is ON for leg corresponding to phase A of the ith microgrid;
- (2)
- If ${I}_{act}^{MG,i}(t)>({I}_{ref}^{*MG,i}(t)+{H}_{B})$, then inverter upper switch is ON, and lower switch is OFF for leg corresponding to phase A of the ith microgrid.

_{B}) can be calculated as in Equation (22). This is obtained by considering switching intervals t

_{1}and t

_{2}as shown in Figure 7, where L

_{a}is phase inductance, ${({I}_{as}^{MG,i})}^{+}$ and ${({I}_{as}^{MG,i})}^{-}$ are rising and falling segments of current. From Figure 7, the following relations can be written as given in Equations (23) and (24):

_{1}and t

_{2}are switching intervals, and f

_{c}is the modulation frequency. By adding Equations (22) and (23) and substituting Equation (24), we arrive at Equation (25). Similarly, by substituting Equations (20)–(22) in Equation (25) and after simplification, we obtain Equation (26).

_{B}) obtained in Equation (30) can be modulated at different instants of frequency to obtain the required gate pulses to the inverter of an ith microgrid.

## 4. Results and Discussion

#### 4.1. Analysis of Voltage Characteristics

#### 4.2. Analysis of Frequency Characteristics

- Switch the inductive load ON at 0.5 s and OFF at 0.8 s;
- Switch the capacitive load ON at 1.3 s and OFF at 1.6 s:
- Observe deviation in case of dynamic loading.

#### 4.3. Analysis of THD

## 5. Conclusions

- ▪
- The proposed FHCC-based inverter is easy to build, as it does not require any clamping diodes and capacitors when compared to conventional configurations. This further reduces the switching losses.
- ▪
- The proposed inverter employs fuzzy logic, which reduces the complexity in mathematical formulation.
- ▪
- From results, the FHCC-based inverter:
- -
- Reduces the voltage sag to 25% when compared with conventional ST-PWM-based inverter (42.5%) and recent FSV-PWM-based inverter (29.5%) when the system is subjected to single line-to-ground fault. Similarly, it reduces the voltage sag to 27.7% when compared with conventional ST-PWM-based inverter (43.37%) and recent FSV-PWM-based inverter (38.6%) when subjected to arcing loads;
- -
- Reduces the voltage swell to 2.5% when compared with conventional ST-PWM-based inverter (4.76%) and recent FSV-PWM-based inverter (2.73%) when subjected to sudden disconnection of major part (75%) of the system load;
- -
- Reduces the voltage unbalance to 2.46% when compared with conventional ST-PWM-based inverter (3.08%) and recent FSV-PWM-based inverter (2.87%) when subjected to large reactive loads injected into the system;
- -
- Reduces the settling time of the system to 0.35 s when compared with conventional ST-PWM-based inverter (0.55 s) and recent FSV-PWM-based inverter (0.42 s);
- -
- Reduces the frequency deviation of the system to 0.3% when compared with conventional ST-PWM-based inverter (1%) and recent FSV-PWM-based inverter (0.45%);
- -
- Reduces the total harmonic distortion of the system to 3.03% when compared with conventional ST-PWM-based inverter (4.29%) and recent FSV-PWM-based inverter (3.85%) when subjected to large resistive loading. Similarly, it reduces the total harmonic distortion of the system to 2.59% when compared with conventional ST-PWM-based inverter (6.38%) and recent FSV-PWM-based inverter (4.73%) for large reactive loading.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

MG | Microgrid | ${\overrightarrow{I}}_{d}^{MG,i}$ | Direct axis current of ith MG in amps |

THD | Total Harmonic Distortion | ${\overrightarrow{I}}_{q}^{MG,i}$ | Quadrature axis current of ith MG in amps |

DG | Distributed Generation | ${\overrightarrow{I}}_{loss}^{MG,i}$ | Loss component of current in ith MG in amps |

PQ | Power quality | ${\overrightarrow{I}}_{d}^{*}$ | Reference source current of d-axis in d-q frame in amps |

$\rho $ | Frequency Droop coefficient | ${\overrightarrow{I}}_{q}^{*}$ | Reference source current of q-axis in d-q frame in amps |

∆f | Change in frequency in Hz | ${I}_{abc,S}^{MG,i}$ | Three-phase source current of ith MG in a-b-c frame in amps |

${V}_{RMS}^{x}$ | Voltage (RMS) at a sampling instant x in volts | ${\overrightarrow{I}}_{\alpha \beta o,S}^{MG,i}$ | Three-phase source current of ith MG in α-β-ο frame in amps |

${V}_{i}^{rms}$ | Voltage (RMS) at ith MG at nth harmonic in volts | ${\overrightarrow{I}}_{abc,S}^{*MG,i}$ | Three-phase source reference current of ith MG in a-b-c frame in amps |

${I}_{i}^{rms}$ | Current (RMS) at ith MG at nth harmonic in amps | ${\overrightarrow{I}}_{\alpha \beta o,S}^{*MG,i}$ | Three-phase source reference current of ith MG in α-β-ο frame in amps |

${V}_{fund}^{rms}$ | Voltage (RMS) at ith MG at fundamental frequency in volts | ${I}_{act}^{MG,i}(t)$ | Actual current of ith MG in amps |

${I}_{fund}^{rms}$ | Current (RMS) at ith MG at fundamental frequency in amps | ${I}_{ref}^{*MG,i}(t)$ | Reference current of ith MG in amps |

${\overrightarrow{I}}_{abc,L}^{MG,i}$ | Three-phase load current of ith MG in amps | H_{B} | Hysteresis band |

${\overrightarrow{V}}_{abc,S}^{MG,i}$ | Three-phase voltage at PCC of ith MG in volts | ${\left({I}_{a}^{MG,i}\right)}^{+}$ | Raising segment of current in phase A in amps |

${V}_{dc}^{*}$ | Reference DC voltage in volts | ${\left({I}_{a}^{MG,i}\right)}^{-}$ | Falling segment of current in phase A in amps |

${V}_{dc}$ | Sensed DC voltage in volts | f_{c} | Modulation frequency in Hz |

## Appendix A

Parameter | Typical Ratings |

Irradiance of PV cell | (150–1000) kW/m^{2} |

Temperature of PV cell | (20–45) °C |

Electric charge (Q) | 1.6 × 10^{−19} Coulombs |

Boltzmann’s constant | 1.3805 × 10^{−23} J/K |

Base power of wind turbine | 1.1 kVA |

Speed of wind | 10 m/s |

Nominal voltage of Ni-cd battery | 88 Volts |

Rated capacity of Ni-cd battery | 6.5 Ah |

Gas constant of fuel cell | 8314.7 |

No of cells in stack of fuel cell | 80 |

Duty cycle of the boost converter | 0.76 |

Switching frequency of the converter | 100 kHz |

Cutoff frequency of low pass filter | 500 Hz |

Transmission line length | 10 Km |

Power of transformer | 300 kVA |

Voltage | 415 Volts |

DC capacitor voltage | 680 Volts |

${K}_{pd}$ | 0.19 |

${K}_{id}$ | 6.25 |

${K}_{pq}$ | 0.19 |

${K}_{iq}$ | 7.5 |

- (1)
- Input variable 1 (error)
- (2)
- Input Variable 2 (Change in error)
- (3)
- Output variables of fuzzy controller
| NB-3: (−1.333 −0.7 −0.3) |

NM-2: (−0.726 −0.354 −0.1372) | |

NM-1: (−0.277 −0.147 0) | |

EZ0: (−0.1 0 0.1) | |

PS + 1: (0 0.18 0.38) | |

PM + 2: (0.18 0.38 0.75) | |

PB + 3: (0.38 0.75 1.33) |

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**Figure 2.**Multilevel inverter configuration, gate pulse generation for one limb, and output voltage. (

**a**) Shows the configuration of multilevel inverter based on ST-PWM; (

**b**) generation of gate pulses for one leg; (

**c**) the output voltage per phase of the ST-PWM-based multilevel inverter.

**Figure 7.**Hysteresis current controller on phase A: (

**a**) structure and (

**b**) voltage-current waveforms.

**Figure 9.**Voltage sag/swell obtained at PCC of cluster microgrids with conventional ST-PWM and proposed FHCC-based inverters subjected to large impedance load.

**Figure 10.**Voltage sag obtained at PCC of cluster microgrids with conventional ST-PWM- and proposed FHCC-based inverters subjected to arc furnace load.

**Figure 11.**Voltage imbalances through positive and negative sequence voltages obtained at PCC of cluster microgrids with conventional ST-PWM- and proposed FHCC-based inverters.

**Figure 12.**Flicker sensation of cluster microgrids at PCC with both with conventional ST-PWM- and proposed FHCC-based inverters.

**Figure 13.**Frequency response of cluster microgrids at PCC with conventional ST-PWM- and proposed FHCC-based inverter subjected to large impedance.

**Figure 14.**Frequency response of cluster microgrids at PCC with conventional ST-PWM- and proposed FHCC-based inverters subjected to large reactive load.

**Figure 15.**Comparison of THD characteristics of cluster microgrids with conventional ST-PWM- and proposed FHCC-based inverter when subjected to large resistive and large reactive load.

S_{1} | S_{2} | S_{3} | S_{4} | S_{5} | S_{6} | S_{7} | S_{8} | V_{AO} | V_{AN} |
---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | V_{dc} | V_{dc}/2 |

0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 3V_{dc}/4 | V_{dc}/4 |

0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | V_{dc}/2 | 0 |

0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | V_{dc}/4 | −V_{dc}/4 |

0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | −V_{dc}/2 |

∆e(n) | N_{-3} | N_{-2} | N_{-1} | E_{0} | P_{1} | P_{2} | P_{3} | |
---|---|---|---|---|---|---|---|---|

e(n) | ||||||||

N_{-3} | N_{-3} | N_{-3} | N_{-3} | N_{-3} | N_{-2} | N_{-1} | N_{-3} | |

N_{-2} | N_{-2} | N_{-3} | N_{-3} | N_{-2} | N_{-1} | E_{0} | N_{-2} | |

N_{-1} | N_{-3} | N_{-3} | N_{-2.} | N_{-1} | E_{0} | P_{1} | N_{-1} | |

E_{0} | N_{-3} | N_{-2} | N_{-1} | E_{0} | P_{1} | P_{2} | E_{0} | |

P_{1} | N_{-2} | N_{-1} | E_{0} | P_{1} | P_{2} | P_{3} | P_{1} | |

P_{2} | N_{-1} | E_{0} | P_{1} | P_{2} | P_{3} | P_{3} | P_{2} | |

P_{3} | E_{0} | P_{1} | P_{2} | P_{3} | P_{3} | P_{3} | P_{3} |

Power Quality Indices | Cluster Microgrids with Conventional ST-PWM-Based Inverter [14] | Cluster Microgrids with Conventional FSV-PWM-Based Inverter [36] | Cluster Microgrids with Proposed FHCC-Based Inverter | Standard Requirements | |
---|---|---|---|---|---|

Voltage Characteristics | Signal shape | Distorted sinewave | Pure sinewave | Pure sinewave | Pure Sinewave |

Sag | 42.5% (violated) | 29.5% | 25% | 40% (IEC 61000-4-11 [28,29]) | |

43.37% (violated) | 38.6% | 27.7% | |||

Swell | 4.76% | 2.73% | 2.5% | ||

Unbalance | 3.08% (violated) | 2.87% | 2.46% | 3% (IEEE 1159.3 [30], EN 50160 [31]) | |

Frequency Characteristics | Settling time | 0.55 s | 0.42 s | 0.35 s | 2% (IEC 61727 [32], IEC 61000-2-2 [33]) |

Deviation (Dynamic load) | 1 | 0.45 | 0.3 | ||

Total Harmonic Distortion (THD) | 4.29% | 3.85% | 3.03% | 5% (IEEE 1547.1 [34], IEEE 519 [35]) | |

6.38% (violated) | 4.73% | 2.59% |

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## Share and Cite

**MDPI and ACS Style**

Kumar, Y.V.P.; Rao, S.N.V.B.; Padma, K.; Reddy, C.P.; Pradeep, D.J.; Flah, A.; Kraiem, H.; Jasiński, M.; Nikolovski, S.
Fuzzy Hysteresis Current Controller for Power Quality Enhancement in Renewable Energy Integrated Clusters. *Sustainability* **2022**, *14*, 4851.
https://doi.org/10.3390/su14084851

**AMA Style**

Kumar YVP, Rao SNVB, Padma K, Reddy CP, Pradeep DJ, Flah A, Kraiem H, Jasiński M, Nikolovski S.
Fuzzy Hysteresis Current Controller for Power Quality Enhancement in Renewable Energy Integrated Clusters. *Sustainability*. 2022; 14(8):4851.
https://doi.org/10.3390/su14084851

**Chicago/Turabian Style**

Kumar, Yellapragada Venkata Pavan, Sivakavi Naga Venkata Bramareswara Rao, Kottala Padma, Challa Pradeep Reddy, Darsy John Pradeep, Aymen Flah, Habib Kraiem, Michał Jasiński, and Srete Nikolovski.
2022. "Fuzzy Hysteresis Current Controller for Power Quality Enhancement in Renewable Energy Integrated Clusters" *Sustainability* 14, no. 8: 4851.
https://doi.org/10.3390/su14084851