# Optimal Distribution Coefficients of Energy Resources in Frequency Stability of Hybrid Microgrids Connected to the Power System

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## Abstract

**:**

## 1. Introduction

## 2. System Modeling and Configuration

#### 2.1. Combined Heat and Power (CHP)

#### 2.2. Synchronous Generator Model

#### 2.2.1. Steam Turbine Model

#### 2.2.2. Excitation System

#### 2.3. Wind Turbine Generator

#### 2.3.1. Rotor Side Converter Vector Control

#### 2.3.2. Grid Side Converter Vector Control

## 3. Optimum Contribution of DERs in Frequency Improvement Scheme

#### 3.1. Multi-Objective Function

#### 3.2. Artificial Bee Colony (ABC) Algorithm

## 4. Simulation Results and Discussion

#### 4.1. Scenario I

#### 4.2. Scenario II

#### 4.3. Scenario III

#### 4.4. Scenario IV

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MG | Microgrid |

RES | Renewable Energy Sources |

FCAS | Frequency Control Ancillary Services |

DER | Distributed Energy Resources |

PEIG | Power Electronic Interferences Generation |

RoCoF | Rate of Change of Frequency |

ABC | Artificial Bee Colony |

DG | Distributed Generation |

CHP | Combined Heat and Power |

WTG | Wind turbine Generator |

WECS | Wind Energy Conversion System |

MPPT | Maximum Power Point Tracking |

PV | Photovoltaic Panles |

LFC | Load Frequency Control |

MOF | Multi-Objective Function |

SG | Synchronous Generator |

DEG | Diesel Engine Generator |

DFIG | Doubly Fed Induction Generator |

GSC | Grid Side Converter |

RSC | Rotor Side Converter |

ISE | Integral Square Error |

KPI | Key Performance Indicator |

GFL | Grid Following |

GFM | Grid Forming |

CIG | Converter Interface Generator |

PCC | Point of Common Coupling |

IGB | Inverter-based Generation Resources |

NSG | Non-synchronous Based Generation |

## References

- Nejabatkhah, F. Overview of control, integration and energy management of microgrids. J. Mod. Power Syst. Clean Energy
**2014**, 2, 212–222. [Google Scholar] - Tayyebi, A.; Groß, D.; Anta, A.; Kupzog, F.; Dörfler, F. Frequency Stability of Synchronous Machines and Grid-Forming Power Converters. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**, 8, 1004–1018. [Google Scholar] [CrossRef] [Green Version] - Ortiz-Villalba, D.; Rahmann, C.; Alvarez, R.; Canizares, C.A.; Strunck, C. Practical Framework for Frequency Stability Studies in Power Systems with Renewable Energy Sources. IEEE Access
**2020**, 8, 202286–202297. [Google Scholar] [CrossRef] - Milano, F.; Dörfler, F.; Hug, G.; Hill, D.J.; Verbič, G. Foundations and Challenges of Low-Inertia Systems (Invited Paper). In Proceedings of the 2018 Power Systems Computation Conference (PSCC), Dublin, Ireland, 11–15 June 2018. [Google Scholar]
- Kenyon, R.W.; Hoke, A.; Tan, J.; Hodge, B. Grid-Following Inverters and Synchronous Condensers: A Grid-Forming Pair. In Proceedings of the 2020 Clemson University Power Systems Conference (PSC), Clemson, SC, USA, 10–13 March 2020; pp. 1–7. [Google Scholar]
- Fernández-Guillamón, A.; Gómez-Lázaro, E.; Muljadi, E.; Molina-García, Á. Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time. Renew. Sustain. Energy Rev.
**2019**, 115, 109369. [Google Scholar] [CrossRef] [Green Version] - Nguyen, H.T.; Yang, G.; Nielsen, A.H.; Jensen, P.H.; Pal, B. Applying Synchronous Condenser for Damping Provision in Converter-Dominated Power System. J. Mod. Power Syst. Clean Energy
**2020**, 9, 639–647. [Google Scholar] [CrossRef] - Ademola-Idowu, A.; Zhang, B. Frequency Stability Using MPC-Based Inverter Power Control in Low-Inertia Power Systems. IEEE Trans. Power Syst.
**2021**, 36, 1628–1637. [Google Scholar] [CrossRef] - Unruh, P.; Nuschke, M.; Strauß, P.; Welck, F. Overview on Grid-Forming Inverter Control Methods. Energies
**2020**, 13, 2589. [Google Scholar] [CrossRef] - Schneider, K.P.; Radhakrishnan, N.; Tang, Y.; Tuffner, F.K.; Liu, C.-C.; Xie, J.; Ton, D. Improving Primary Frequency Response to Support Networked Microgrid Operations. IEEE Trans. Power Syst.
**2019**, 34, 659–667. [Google Scholar] [CrossRef] - Abazari, A.; Dozein, M.G.; Monsef, H. A New Load Frequency Control Strategy for an AC Micro-grid: PSO-based Fuzzy Logic Controlling Approach. In Proceedings of the 2018 Smart Grid Conference (SGC), Sanandaj, Iran, 28–29 November 2018; pp. 1–7. [Google Scholar]
- Abazari, A.; Dozein, M.G.; Monsef, H.; Wu, B. Wind turbine participation in micro-grid frequency control through self-tuning, adaptive fuzzy droop in de-loaded area. IET Smart Grid
**2019**, 2, 301–308. [Google Scholar] [CrossRef] - Abazari, A.; Soleymani, M.M.; Babaei, M.; Ghafouri, M.; Monsef, H. High penetrated renewable energy sources-based AOMPC for microgrid’s frequency regulation during weather changes, time-varying parameters and generation unit collapse. IET Gener. Transm. Distrib.
**2020**, 14, 5164–5182. [Google Scholar] [CrossRef] - Rakhshani, E.; Rodriguez, P. Active power and frequency control considering large scale RES. In Large Scale Renewable Power Generation: Advances in Technologies for Generation Transmission and Storage; Springer: Singapore, 2013. [Google Scholar]
- Gu, H.; Yan, R.; Saha, T.K. Minimum Synchronous Inertia Requirement of Renewable Power Systems. IEEE Trans. Power Syst.
**2018**, 33, 1533–1543. [Google Scholar] [CrossRef] [Green Version] - Alaboudy, A.H.K.; Zeineldin, H.H.; Kirtley, J.L. Microgrid stability characterization subsequent to fault-triggered islanding incidents. IEEE Trans. Power Del.
**2012**, 27, 658–669. [Google Scholar] [CrossRef] - Oshnoei, A.; Kheradmandi, M.; Muyeen, S.M. Robust control scheme for distributed battery energy storage systems in load frequency control. IEEE Trans. Power Syst.
**2020**, 35, 4781–4791. [Google Scholar] [CrossRef] - Meegahapola, L.; Flynn, D. Impact on transient and frequency stability for a power system at very high wind penetration. In Proceedings of the IEEE PES General Meeting, Minneapolis, MN, USA, 24–28 June 2010; pp. 1–8. [Google Scholar]
- Oshnoei, A.; Kheradmandi, M.; Muyeen, S.M.; Hatziargyriou, N. Disturbance Observer and Tube-based Model Predictive Controlled Electric Vehicles for Frequency Regulation of an Isolated Power Grid. IEEE Trans. Smart Grid.
**2021**, 10, 1. [Google Scholar] [CrossRef] - Lal, D.K.; Barisal, A.K. Load frequency control of AC microgrid interconnected thermal power system. IOP Conf. Ser. Mater. Sci. Eng.
**2017**, 225, 012090. [Google Scholar] [CrossRef] - Cam, E.; Kocaarslan, I. Load frequency control in two area power systems using fuzzy logic controller. Energy Convers. Manag.
**2005**, 46, 233–243. [Google Scholar] [CrossRef] - Schonbergerschonberger, J.; Duke, R.; Round, S.D. DC-bus signaling: A distributed control strategy for ahybrid. IEEE Trans. Ind. Electron.
**2006**, 53, 1453–1460. [Google Scholar] [CrossRef] - Khooban, M.H.; Niknam, T.; Blaabjerg, F.; Davari, P. A robust adaptive load frequency control for micro-grids. ISA Trans.
**2016**, 65, 220–229. [Google Scholar] [CrossRef] [PubMed] - Yang, J.; Zhili, Z.; Yufei, T.; Jun, Y.; Haibo, H.; Yunliang, W. Load frequency control in isolated micro-grids with electrical vehicles based on multivariable generalized predictive theory. Energies
**2015**, 8, 2145–2164. [Google Scholar] [CrossRef] - Zhang, S.; Tang, T.; Song, B.; Lu, S.; Ye, B. Stable adaptive PI control for permanent magnet synchronous motor drive based on improved JITL technique. ISA Trans.
**2013**, 54, 539–549. [Google Scholar] [CrossRef] [PubMed] - Yaseli:, E. Interval type-2 fuzzy PID load frequency controller using big bang-big crunch optimization. App. Soft. Comp.
**2014**, 15, 100–112. [Google Scholar] - Massucco, S.; Pitto, A.; Silvestro, F. A gas turbine model for studies on distributed generation penetration into distribution networks. IEEE Trans. Power Syst.
**2011**, 26, 992–999. [Google Scholar] [CrossRef] - Sun, T.; Lu, J.; Li, Z.; Lubkeman, D.L.; Lu, N. Modeling Combined Heat and Power Systems for Microgrid Applications. IEEE Trans. Smart Grid
**2018**, 9, 4172–4180. [Google Scholar] [CrossRef] - Hossein, J.M.; Pota, H.R.; Mahmud, M.A.; Aldeen, M. Robust control for power sharing in microgrids with low-inertia wind and PV generators. IEEE Trans. Sustain. Energy
**2015**, 6, 1067–1077. [Google Scholar] [CrossRef] - Abazari, A.; Dozein, M.G.; Monsef, H. An optimal fuzzy-logic based frequency control strategy in a high wind penetrated power system. J. Frankl. Inst.
**2018**, 355, 6262–6285. [Google Scholar] [CrossRef] - Abazari, A.; Monsef, H.; Wu, B. Load frequency control by de-loaded wind farm using the fuzzy-based PID droop controller. IET Renew. Power Generat.
**2018**, 13, 180–190. [Google Scholar] [CrossRef] - Vidyanandan, K.V.; Senroy, N. Primary frequency regulation by deloaded wind turbines using variable droop. IEEE Trans. Power Syst.
**2013**, 28, 837–846. [Google Scholar] [CrossRef] - Datta, M.; Senju, T. Fuzzy control of distributed PV inverters/energy storage systems/ electric vehicles for frequency regulation in a large power system. IEEE Trans. Smart Grid
**2013**, 1, 479–488. [Google Scholar] [CrossRef] - Taghizadeh, M.; Mardaneh, M.; Sadeghi, M.S. Frequency control of a new topology in proton exchange membrane fuel cell/wind turbine/photovoltaic/ultra capacitor/ battery energy storage system based isolated networks by a novel intelligent controller. J. Renew. Sustain. Energy
**2014**, 6, 53121. [Google Scholar] [CrossRef] - Oshnoei, A.; Kheradmandi, M.; Oshnoei, S. Optimal model predictive control of photovoltaic plants for frequency regulation in an interconnected power system. In Proceedings of the 34th International Power System Conference (PSC), Tehran, Iran, 9–11 December 2019; pp. 428–433. [Google Scholar]
- Machowski, J.; Lubosny, Z.; Bialek, J.; Bumby, J.R. Power System Dynamics: Stability and Control; Wiley: Hoboken, NJ, USA, 2020. [Google Scholar]
- Kundur, P.; Balu, N.J.; Lauby, M.G. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994. [Google Scholar]
- Task Force on Turbine Governor Modeling; Power System Dynamic Performance Committee; Power System Stability Subgroup. Dynamic Models for Turbine-Governors in Power System Studies. Available online: https://resourcecenter.ieee-pes.org/publications/technical-reports/PESTR1.html (accessed on 2 June 2021).
- IEEE Recommended Practice for Excitation System Models for Power System Stability Studies. Available online: https://www.semanticscholar.org/paper/IEEE-recommended-practice-for-excitation-system-for-Board/05bc9ef274285d8be39c5aa0ff9fe0611a6c7874 (accessed on 5 June 2021).
- Tapia, G.; Tapia, A.; Ostolaza, J.X. Two alternative modeling approaches for the evaluation of wind farm active and reactive power performance. IEEE Trans. Energy Convers.
**2006**, 21, 909–920. [Google Scholar] [CrossRef] - Boldea, I. Variable Speed Generator; Taylor & Francis Group: New York, NY, USA, 2006. [Google Scholar]
- Xing, P.; Fu, L.; Wang, G.; Wang, Y.; Zhang, Y. A compositive control method of low-voltage ride through for PMSG-based wind turbine generator system. Gener. Transm. Distrib. IET
**2018**, 12, 117–125. [Google Scholar] [CrossRef] - Pena, R.; Clare, J.C.; Asher, G.M. Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. Proc. Inst. Elect. Eng.
**1996**, 143, 231–241. [Google Scholar] [CrossRef] [Green Version] - Qiao, W.; Zhou, W.; Aller, J.M.; Harley, R.G. Wind speed estimation based sensorless output maximization control for a wind turbine driving a DFIG. IEEE Trans. Power Electron.
**2008**, 23, 1156–1169. [Google Scholar] [CrossRef] - Karaboga, D.; Basturk, B. A powerful and efficient algorithm for numerical optimization: Artificial bee colony (ABC). J. Glob. Optim.
**2007**, 39, 459–471. [Google Scholar] [CrossRef]

**Figure 9.**The layout of hybrid MG connected to a power system using distribution coefficients in frequency excursion improvement.

**Figure 14.**(

**a**) CHP unit power delivered for different load steps. (

**b**) Active power injection by diesel engine generator during various load steps. (

**c**) Wind farm power injection during various load steps. (

**d**) Solar panel power injection during various load steps.

**Figure 15.**Frequency deviation due to 10% load disconnection in the presence of different DER contributions.

**Figure 16.**Frequency devotion due to the 30% reduction in system inertia for different combinations of inverter-based and droop-based strategies.

**Figure 17.**Frequency deviation due to the 10% load changes in the presence of different combinations of inverter-based and droop-based strategies.

**Figure 18.**Rate of Change of Frequency (RoCoF) intended for various combinations of droop- and inverter-based structures during the –10% load step change.

**Figure 19.**Frequency deviation during 100 MW SG outage in the presence of different values of inertia constants.

**Figure 20.**(

**a**) Active power injected by CHP in the islanded MG unit during various inertia constants. (

**b**) Diesel Unit Power Delivery for different Inertia-100 MW SG Loss. (

**c**) Wind farm Unit Power Delivery for different Inertia-100 MW SG Loss. (

**d**) Solar Unit Power Delivery for different Inertia-100 MW SG Loss.

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

Proportional gain | ${\mathrm{K}}_{\mathrm{p}}$ | 40 |

Integral time constant | ${\mathrm{K}}_{\mathrm{i}}$ | 0.2 |

Lead–Lag time constant | ${\mathrm{T}}_{1}-{\mathrm{T}}_{2}$ | 0.2 |

Turbine time constant | ${\mathrm{T}}_{3}-{\mathrm{T}}_{4}$ | 0.1 |

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

Rated RMS line-neutral voltage | ${\mathrm{V}}_{\mathrm{base}}$ | 66.47 [kV] |

Rated RMS line current | ${\mathrm{I}}_{\mathrm{base}}$ | 0.7 [kA] |

Inertia constant | $\mathrm{H}$ | 3.85 [s] |

Mechanical friction | $\mathrm{D}$ | 0.01 [pu] |

Armature resistance | ${\mathrm{R}}_{\mathrm{a}}$ | 0.003 [pu] |

Poitier reactance | ${\mathrm{X}}_{\mathrm{p}}$ | 0.11 [pu] |

Unsaturated reactance | ${\mathrm{X}}_{\mathrm{d}}$ | 1.79 [pu] |

Unsaturated transient reactance | ${\mathrm{X}}_{\mathrm{d}}^{\prime}$ | 0.24 [pu] |

Unsaturated transient time (Open) | ${\mathrm{T}}_{\mathrm{do}}^{\prime}$ | 5.9 [s] |

Unsaturated sub-transient reactance | ${\mathrm{X}}_{\mathrm{d}}^{\u2033}$ | 0.185 [pu] |

Unsaturated sub-transient time (Open) | ${\mathrm{T}}_{\mathrm{do}}^{\prime}$ | 0.033 [s] |

Unsaturated reactance | ${\mathrm{X}}_{\mathrm{q}}$ | 1.64 [pu] |

Unsaturated transient reactance | ${\mathrm{X}}_{\mathrm{q}}^{\prime}$ | 0.38 [pu] |

Unsaturated transient time (Open) | ${\mathrm{T}}_{\mathrm{qo}}^{\prime}$ | 0.54 [s] |

Unsaturated sub-transient reactance | ${\mathrm{X}}_{\mathrm{q}}^{\u2033}$ | 0.185 [pu] |

Unsaturated sub-transient time (Open) | ${\mathrm{T}}_{\mathrm{qo}}^{\u2033}$ | 0.076 [s] |

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

Steam chest time constant | ${\mathrm{T}}_{4}$ | 0.2 |

Reheater time constant | ${\mathrm{T}}_{5}$ | 0.2 |

Reheater/cross-over time constant | ${\mathrm{T}}_{6}$ | 1.0 |

Over-heater time constant | ${\mathrm{T}}_{7}$ | 1.0 |

Turbine (HP + LP) initial output power | ${\mathrm{P}}_{\mathrm{mo}}$ | 1.0 |

Different fraction for LP and HP stages(p.u.) | ${\mathrm{K}}_{1}-{\mathrm{K}}_{8}$ | 0.125 |

Description. | Symbol | Value |
---|---|---|

Lead time constant | ${\mathrm{T}}_{\mathrm{C}}$ | 1.0 s |

Lag time constant | ${\mathrm{T}}_{\mathrm{B}}$ | 10 s |

Regulator integral gain | ${\mathrm{K}}_{\mathrm{A}}$ | 200 p.u. |

Regulator time constant | ${\mathrm{T}}_{\mathrm{A}}$ | 0.015 |

Rectifier loading factor | ${\mathrm{K}}_{\mathrm{C}}$ | 0.2 p.u. |

Transducer time constant | ${\mathrm{T}}_{\mathrm{R}}$ | 0.1 s |

Upper limit on error signal | ${\mathrm{V}}_{\mathrm{IMAX}}$ | 10 |

Lower limit on error signal | ${\mathrm{V}}_{\mathrm{IMIN}}$ | −10 |

Maximum regulator output | ${\mathrm{V}}_{\mathrm{RMAX}}$ | 5.64 |

Minimum regulator output | ${\mathrm{V}}_{\mathrm{RMIN}}$ | −4.53 |

WTG Parameters. | Symbol | Values |

Rated power | ${\mathrm{P}}_{\mathrm{base}}$ | 15 MW |

LL Voltage | ${\mathrm{V}}_{\mathrm{base}}$ | 0.69 kV |

Base Angular Frequency | ${\mathrm{f}}_{\mathrm{main}}$ | 60 Hz |

Stator/Rotor turns ratio | $\mathrm{TRN}$ | 0.85 |

Angular moment of inertia(j = 2 h) | ${\mathrm{J}}_{\mathrm{WTG}}$ | 0.6 |

Mechanical Damping | ${\mathrm{D}}_{\mathrm{WTG}}$ | 0.0001 p.u |

Stator Resistance | R_{1} | 0.0054 p.u |

Wound rotor resistance | R_{2} | 0.00607 p.u |

First Squirrel cage resistance | R_{3} | 0.298 p.u |

Magnetizing Inductance | ${\mathrm{X}}_{\mathrm{md}}$ | 4.5 |

Stator leakage inductance | ${\mathrm{X}}_{\mathrm{a}}$ | 0.10 |

Wound rotor Leakage inductance | ${\mathrm{X}}_{\mathrm{kd}1}$ | 0.11 |

First Cage Leakage Inductance | ${\mathrm{X}}_{\mathrm{kd}2}$ | 0.05 |

Converter Parameters | Symbol | Values |

Convertor reactor | ${\mathrm{L}}_{\mathrm{conv}}$ | 0.00134 H |

Capacitance | ${\mathrm{C}}_{\mathrm{dc}}$ | 50,000 μF |

Machine terminal Voltage | ${\mathrm{V}}_{\mathrm{LL}}$ | 0.69 KV |

Stator resistance | ${\mathrm{R}}_{\mathrm{st}}$ | 0.0054 p.u |

Total System Inertia | Reduced Inertia | ΔP(MW) Response Requirement | ||||
---|---|---|---|---|---|---|

Based on the Second | Utility Grid | Droop-Based DERs | 50 MW SG Loss (42% of Total Capacity) | 100 MW SG Loss (55% of Total Capacity) | 300 MW SG Loss (59% of Total Capacity) | 100 MW Load Step (83% of Total Load) |

15 | ✓ | ✓ | 59 MW | 100 MW | 215 MW | 98 MW |

8-Normal | 54 MW | 99 MW | 214 MW | 103 MW | ||

6 | ✓ | 55 MW | 99 MW | 216 MW | 103.5 MW | |

5 | ✓ | 54 MW | 100 MW | 203 MW | 104 MW | |

2 | ✓ | ✓ | 54 MW | 102 MW | 206 MW | 104 MW |

H(s) | SG | Diesel Generator | CHP |
---|---|---|---|

15 | 4.96 | 4.96 | 4.96 |

8 | 3.96 | 1.96 | 2.31 |

6 | 1.73 | 1.96 | 2.31 |

5 | 3.96 | 0.5 | 0.5 |

2 | 1.0 | 0.5 | 0.5 |

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**MDPI and ACS Style**

Arzani, M.; Abazari, A.; Oshnoei, A.; Ghafouri, M.; Muyeen, S.M.
Optimal Distribution Coefficients of Energy Resources in Frequency Stability of Hybrid Microgrids Connected to the Power System. *Electronics* **2021**, *10*, 1591.
https://doi.org/10.3390/electronics10131591

**AMA Style**

Arzani M, Abazari A, Oshnoei A, Ghafouri M, Muyeen SM.
Optimal Distribution Coefficients of Energy Resources in Frequency Stability of Hybrid Microgrids Connected to the Power System. *Electronics*. 2021; 10(13):1591.
https://doi.org/10.3390/electronics10131591

**Chicago/Turabian Style**

Arzani, Mohsen, Ahmadreza Abazari, Arman Oshnoei, Mohsen Ghafouri, and S. M. Muyeen.
2021. "Optimal Distribution Coefficients of Energy Resources in Frequency Stability of Hybrid Microgrids Connected to the Power System" *Electronics* 10, no. 13: 1591.
https://doi.org/10.3390/electronics10131591