# A New Robust Control Strategy for Parallel Operated Inverters in Green Energy Applications

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- The degree of issue mainly relies on the size of DC-link capacitance, which is chosen traditionally in order to deal with certain filter requirements like to decrease voltage fluctuation cause by switching current.
- Even though the above-mentioned studies stressed on enhancing transient dynamics pertaining to the average power control, not a single study was able to address the instantaneous transient power impact on parallel inverters’ stability. Moreover, not a single study regarded the impact cast by mismatched line impedances on the damping and circulated power of the microgrid system.

- Hierarchical control structure has been recommended for both frequency and voltage restoration pertaining to grid-connected microgrid as well as islanded microgrid by accounting for the complete nonlinear system model, regardless of the parametric disturbances as well as uncertainties.
- The impact pertaining to mismatched line impedances has been evaluated based on the performance of parallel inverters that were supplied by various energy sources, and it also investigates the instantaneous circulating power responses against microgrid’s stability. In addition, the system has been analyzed by employing microgrid’s small signal state space model that includes three inverters. In order to uphold microgrid’s stability, we recommend employing two controller schemes that account for supplementary phase as well as frequency loops. The most effective controller scheme possessing the least action linked with DC- link voltage have been employed for participation factor assessment. Simulation was applied to validate the proposed controller.
- Distributed consensus-based control scheme has been suggested to precisely carry out power sharing when there is frequency restoration. The proposed strategy can be regarded as fully distributed method that allows distributing communication and computational tasks amongst local controllers by working in parallel, which is also more scalable, flexible and insusceptible to single point failure.
- Hybrid microgrid has been studied by accounting for typical energy storage systems, unbalanced and balanced load switch and nonlinear and linear loads offered via description of model containing all necessary data to deal with the aforementioned studies.

## 2. Proposed System Description

## 3. Microgrid Control Methods

#### 3.1. The Primary Control

#### 3.2. Secondary Control Layer

- (1)
- Centralized control: It is based on a central controller that requires one to all communication scheme. The central controller computes all components errors, using measurements from the PCC (Point of Common Coupling), and sends the corrective term to the other converters. This is a robust technique against communication constraints, however with low reliability (network is completely central dependent), tolerance and flexibility in case of fault of the converter, demanding controller duplication due to its master-slave configuration.
- (2)
- Decentralized control: It is a hybrid system based on local and central controllers, that requires one to all communication schemes. As in the former technique, the signals errors are common to the inverters obtained by the central controller, but further properties as the corrective term are autonomously computed by each local controller. This technique is sensitive to communication issues, since the inverters can produce different corrective terms if receiving information in distinct time due to non-synchronized internal clocks between controllers, an effect known as clock drift.

#### 3.3. Tertiary Control

## 4. Distributed Hybrid Energy Generation System

#### 4.1. Modelling of Photovoltaic Cell

^{−23}J/K, q is electron charge (1.602 × ${10}^{-19}$ C), ${R}_{p,cell}$ is parallel resistance of photovoltaic, ${R}_{s,cell}$, is series resistance of photovoltaic.

#### 4.2. Modelling of Photovoltaic Module

^{2}irradiance and 25 °C temperature), $\mathsf{\Delta}T$ refers to the difference between the PV cell’s actual temperature ($T$) and the nominal temperature (${T}_{n}$) measured in °C, ${G}_{n}$ is the nominal irradiance (1000 w/m

^{2}), $G$ is the measured solar irradiance in w/m

^{2}${K}_{i}$ is temperature coefficient. The open voltage circuit (${V}_{oc}$) is affected by the cell temperature based on the following equation:

#### 4.3. Battery Storage System

#### 4.4. Wind Turbine Model

^{3}, ${V}_{w}$ is wind speed, ${C}_{p}\left(\lambda .\text{}\beta \right)$ is performance coefficient of the wind turbine. The wind turbine performance factor (${C}_{p}$) depends on the blade aerodynamics and depicts the wind turbine’s efficiency. One can describe the performance factor as follows:

#### 4.5. Concept of Stability

#### 4.5.1. Microgrid Stability Classification

#### 4.5.2. Stability of Islanded Microgrid

## 5. Dynamic Analysis of the System

_{O}and an output impedance (${R}_{O}+j\omega {L}_{O}$). Figure 10 illustrates an islanded configuration of a microgrid. Each inverter is fitted with two cascaded space models. The first model shows the power-sharing controller while the second model represents the output impedance.

#### 5.1. System Power-Sharing

#### 5.2. Output Impedance Model

#### 5.3. Distribution Lines Model

#### 5.4. Loads Model

#### 5.5. Model of Inverters

_{p}is similar, the corresponding eigenvalues represent varying damping ratios, with poles observed to shift from their original locations. This can lead to an increase in overshoot and oscillations. In both figures, the eigenvalues at ${m}_{p}=3\times {10}^{-3}$ are emphasized to signify that the same droop gain generates varying damping ratios of output power responses. It is desirable to increase ${m}_{P}$ in order to obtain high sharing accuracy. This, however, degrades stability.

## 6. Control Strategy for PV/Wind/Storage Energy System

#### 6.1. Controller of the Converter Interfacing Photovoltaic

#### 6.2. Controller of the Converter Interfacing WT

#### 6.3. Controller of Bidirectional Converter Interfacing Batteries

## 7. Proposed Controller to Limit DC-Link Voltage

## 8. Analysis of the Participation Factor

## 9. The Controller Design

- The increase in the proposed gain of control (${P}_{dc})$ affects targeted eigenvalues ${\lambda}_{20}$, ${\lambda}_{21}$, ${\lambda}_{23}$, in alignment with that displayed in Table 6. Nevertheless, certain other eigenvalues are similarly affected, namely ${\lambda}_{14}$, ${\lambda}_{15}$, ${\lambda}_{16}$, ${\lambda}_{17}$, as couplings between eigenvalues and state variables cannot be easily analysed. In addition, the targeted ${\lambda}_{25}$ demonstrates negligible change, for it is mostly subject to determining filter bandwidth, in which ${\lambda}_{18}$, ${\lambda}_{19}$, ${\lambda}_{24}$, are not influenced.
- Increased ${P}_{dc}$ movement targets eigenvalues farther to the left and therefore increases damping of system. Nevertheless, high frequency eigenvalue similarly move towards imaginary axis, whereby at certain higher gains, system instability ensues.

## 10. Simulation Results

_{dc}= 0.001. The system is unstable and oscillation frequency is 314 rad/second, this is consistent with the prediction in Figure 18 as the system becomes unstable and oscillation frequency is 312 rad/second.

## 11. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) ω–P droop characteristics of a microgrid and (

**b**) V–P droop characteristics of microgrid.

**Figure 11.**The eigenvalues of system, 5 × 10

^{−5}m

_{p}5 × 10

^{−3}where (

**a**) lines inductances neglected, (

**b**) when L_Line1 = 10

^{−3}H and L_Line1 = 2 × 10

^{−3}H.

**Figure 12.**Simulation of identical distribution lines are used, (

**a**) inverters power response, (

**b**) DC link voltage response under loads change.

**Figure 13.**Simulation of different distribution lines are used, (

**a**) the inverters power response, (

**b**) DC link voltage response under loads change.

**Figure 19.**Simulation of loads change, where (

**a**) active power responses, (

**b**) responses of DC-link voltage.

**Figure 20.**Simulation result, where (

**a**) the averaged power response, (

**b**) response of DC link voltage.

**Figure 21.**The method shown in Figure 17a is used, where (

**a**) is the response of averaged power, (

**b**) is the DC link voltage response.

Parameters | Value |
---|---|

Series connected modules | $7$ |

Parallel string | $1$ |

Voltage of open circuit $\left({V}_{oc}\right)$ | 6.42 (V) |

Maximum voltage $\left({V}_{mp}\right)$ | 54.7 (V) |

Temperature coefficient of $\left({V}_{oc}\right)$ | −0.27269 (%/°C) |

Short-circuit current $\left({I}_{sc}\right)$ | 5.96 (A) |

Maximum current ${I}_{mp}$ | 5.58 (A) |

Temperature coefficient of $\left({I}_{sc}\right)$ | 0.061745 (%/°C) |

Shunt resistance $\left({R}_{sh}\right)$ | 269.5934 Ω |

Series resistance $\left({R}_{s}\right)$ | 0.37152 Ω |

Diode ideality factor | 0.945 |

Diode saturation curent ${I}_{o}$ | $6.3\times {10}^{-1}$ (A) |

PV type | SPR-305E-WHT-D |

Number of cells | 96 |

Parameters | Value | Unit |
---|---|---|

Total inertia (J) | $0.0119$ | Kg·m^{2} |

The state friction | 5 | N·m |

Viscous friction coefficient (F) | $0.001189$ | N·m·s |

Inductance of d-axis | 0.0082 | H |

Resistance of Stator | 0.42 | Ω |

Inductance of q-axis | 0.0082 | H |

Number of phases | 3 | N |

Wind speed | 12 | m/s |

Performance factor $\left({C}_{p}\right)$ | 0.48 | C |

Pitch angle (β) | 0 | degree |

air density $\left(\rho \right)$ | 1.225 | Kg/m^{3} |

Base rotational speed | 1.2 | pu |

${\omega}_{e}$ | 376 | rad/sec |

Parameters | Values | Units |
---|---|---|

inductance of d-axis | 0.0082 | H |

Resistance of Stator | 0.42 | Ω |

inductance of q-axis | 0.0082 | H |

${\mathrm{V}}_{\mathrm{pk}}/\mathrm{Krpm}$ | 98.7 | - |

Number of poles | 8 | - |

Mechanical time | 0.04 | - |

Inertia Moment | 8 × 10^{−3} | N–msec^{2} |

Eigenvalues | Locations | Eigenvalues | Locations |
---|---|---|---|

${\lambda}_{1}$ | 0.0 | ${\lambda}_{14}$ | −151 + 318 i |

${\lambda}_{2}$ | 0.0 | ${\lambda}_{15}$ | −151 − 318 i |

${\lambda}_{3}$ | 0.0 | ${\lambda}_{16}$ | −90 + 318 i |

${\lambda}_{4}$ | −224,683,637 + 316 i | ${\lambda}_{17}$ | −90 − 318 i |

${\lambda}_{5}$ | −224,683,637 − 316 i | ${\lambda}_{18}$ | −4 |

${\lambda}_{6}$ | −224,683,637 + 316 i | ${\lambda}_{19}$ | −6 |

${\lambda}_{7}$ | −224,683,637 − 316 i | ${\lambda}_{20}$ | −20 + 7 i |

${\lambda}_{8}$ | −2,546,836 + 316 i | ${\lambda}_{21}$ | −20 − 7 i |

${\lambda}_{9}$ | −2,546,836 − 316 i | ${\lambda}_{22}$ | −23 |

${\lambda}_{10}$ | −693,417 + 316 i | ${\lambda}_{23}$ | −25 |

${\lambda}_{11}$ | −693,417 − 316 i | ${\lambda}_{24}$ | −31 |

${\lambda}_{12}$ | −31,719 + 316 i | ${\lambda}_{25}$ | −31 |

${\lambda}_{13}$ | −31,719 − 316 i | ${\lambda}_{26}$ | 0 |

Mode/State | $\Delta {\mathit{\delta}}_{1}$ | $\Delta {\mathit{P}}_{1}$ | $\Delta {\mathit{\delta}}_{2}$ | $\Delta {\mathit{P}}_{2}$ | $\Delta {\mathit{\delta}}_{3}$ | $\Delta {\mathit{P}}_{3}$ |
---|---|---|---|---|---|---|

${\lambda}_{20,21}$ | 0.34 | 0 | 0.64 | 0 | 0.03 | 0 |

${\lambda}_{23}$ | 0.34 | 0 | 0.03 | 0 | 0.61 | 0 |

${\lambda}_{25}$ | 1.01 | 0 | 0 | 0 | 0 | 0 |

State | ${\mathit{\lambda}}_{14,\text{}15}$ | ${\mathit{\lambda}}_{16,\text{}17}$ | ${\mathit{\lambda}}_{18}$ | ${\mathit{\lambda}}_{19}$ | ${\mathit{\lambda}}_{20,\text{}21}$ | ${\mathit{\lambda}}_{22}$ | ${\mathit{\lambda}}_{23}$ | ${\mathit{\lambda}}_{24}$ | ${\mathit{\lambda}}_{25}$ |
---|---|---|---|---|---|---|---|---|---|

$\Delta {\delta}_{1}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta {P}_{1}$ | 0.002 | 0 | 0.07 | 0.1 | 0.2 | 0.1 | 0.6 | 0.1 | 0.5 |

$\Delta {Q}_{1}$ | 0.008 | 0 | 0 | 0.07 | 0.1 | 0.42 | 0.09 | 0.5 | 0.07 |

$\Delta io{d}_{1}$ | 0.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta io{q}_{1}$ | 0.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta {\delta}_{2}$ | 0.001 | 0 | 0.08 | 1.2 | 0.5 | 0 | 0.03 | 0 | 0 |

$\Delta {P}_{2}$ | 0 | 0 | 0.01 | 0.2 | 0.5 | 0 | 0.07 | 0.01 | 0.35 |

$\Delta {Q}_{2}$ | 0.014 | 0 | 0 | 0.14 | 0.2 | 0 | 0.01 | 0.3 | 0.07 |

$\Delta io{d}_{2}$ | 0.2 | 00 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta io{q}_{2}$ | 0.2 | 0 | 0 | 0.009 | 0 | 0 | 0 | 0 | 0 |

$\Delta {\delta}_{3}$ | 0 | 0 | 1.3 | 0.083 | 0.04 | 0.15 | 0.45 | 0 | 0 |

$\Delta {P}_{3}$ | 0 | 0 | 0.16 | 0.017 | 0.04 | 0.26 | 1 | 0.1 | 0.5 |

$\Delta {Q}_{3}$ | 0.001 | 0 | 0 | 0.01 | 0.017 | 0.77 | 0.18 | 0.4 | 0.07 |

$\Delta io{d}_{3}$ | 0.016 | 0.11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta io{q}_{3}$ | 0.016 | 0.11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta iolin{e}_{D1}$ | 0.1 | 0.07 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta iolin{e}_{Q1}$ | 0.1 | 0.2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta iolin{e}_{D2}$ | 0.03 | 0.2 | 0 | 0 | 0 | 0.01 | 0 | 0 | 0 |

$\Delta iolin{e}_{Q2}$ | 0.03 | 0 | 0 | 0 | 0 | 0.01 | 0 | 0 | 0 |

$\Delta ioloa{d}_{D1}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta ioloa{d}_{Q1}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta ioloa{d}_{D2}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta ioloa{d}_{Q2}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta vd{c}_{1}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta vd{c}_{2}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

$\Delta vd{c}_{3}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Symbols | Descriptions | Values |
---|---|---|

${L}_{o,i}$${R}_{o,i}$ | Output impedance of inverter | $1\mathrm{mH}$, $1\times {10}^{-1}$ Ω |

${L}_{line,1}$, ${R}_{line,1}$ | Impedance of line1 | $1\text{}\mathrm{mH}$, $2\times {10}^{-3}$ Ω |

${L}_{line,2}$, ${R}_{line,2}$ | Impedance of line2 | $2\text{}\mathrm{mH}$, $3\times {10}^{-3}$ Ω |

${m}_{p}$ | Droop gain frequency | 10^{-3} rad/s |

${n}_{q}$ | Droop gain voltage | ${10}^{-3}$ |

${V}_{o}$ | Set point voltage | 110 V_{rms} |

${f}_{o}$ | Set point frequency | 50 Hz |

${\omega}_{c}$ | Cut off frequency of filter | $30\text{}\mathrm{rad/s}$ |

${V}_{DC-Link}$ | Voltage of DC link | 200 V |

${V}_{trip}$ | Trip voltage of DC link | 280 V |

${V}_{tr}$ | Voltage of Triggering | 215 V |

${K}_{dc}$ | Linearization factor | $2.4$ |

${C}_{dc\_link}$ | Capacitor of Dc-Link | 2 mF |

${P}_{dc}$ | Controller gain | 5 × ${10}^{-4}$ |

© 2020 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**

Alhasnawi, B.N.; Jasim, B.H.; Issa, W.; Anvari-Moghaddam, A.; Blaabjerg, F.
A New Robust Control Strategy for Parallel Operated Inverters in Green Energy Applications. *Energies* **2020**, *13*, 3480.
https://doi.org/10.3390/en13133480

**AMA Style**

Alhasnawi BN, Jasim BH, Issa W, Anvari-Moghaddam A, Blaabjerg F.
A New Robust Control Strategy for Parallel Operated Inverters in Green Energy Applications. *Energies*. 2020; 13(13):3480.
https://doi.org/10.3390/en13133480

**Chicago/Turabian Style**

Alhasnawi, Bilal Naji, Basil H. Jasim, Walid Issa, Amjad Anvari-Moghaddam, and Frede Blaabjerg.
2020. "A New Robust Control Strategy for Parallel Operated Inverters in Green Energy Applications" *Energies* 13, no. 13: 3480.
https://doi.org/10.3390/en13133480