# Electromechanical Design of Synchronous Power Controller in Grid Integration of Renewable Power Converters to Support Dynamic Stability

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## Abstract

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## 1. Introduction

## 2. Structure and Control of RSSG-SPC

## 3. Internal Dynamics of RSSG-SPC

- (i)
- ${\lambda}_{SSG}$ are oscillatory. This means RSSG-SPC is not completely stiff from the dynamic point of view, therefore RSSG-SPC can act as a strong dynamic damper, as well as it can respond to oscillations inside the external power grid.
- (ii)
- ${\lambda}_{SSG}$ has a significant level of damping ratio (${\xi}_{SSG}=0.70\text{}\mathrm{pu}$). This means the internal dynamics of RSSG-SPC has enough damping and it can share damping with the external power grid. This also means this dynamic damper is strong enough.
- (iii)
- The dynamic modes are in the condition that RSSG-SPC’s time response is acceptable for control and damp the oscillations. This means the electromechanical parts has a fast reaction to the oscillation in the external power grid.

## 4. Small Signal Modelling of Power Network in Presence of RSSG-SPC

- (i)
- The first sub-group of equations has been explained in Equations (19)–(23). These equations clarify the electrical link between the generation units and other parts of the power grid. In this sub-group, the linear link between the active power of each generation unit (${P}_{ei}$) and its respective power angle (${\delta}_{i}$) has been defined. The first equation of Equation (19) shows the output active power of each generation unit where the internal voltage and transient reactance are fixed ($\mathsf{\Delta}{X}_{di}^{\prime}$, $\mathsf{\Delta}{\overline{E}}_{i}=0$). The linearization process can be done using the second equation of Equation (19), then the results of linearization can be written in the matrix format as last equation of Equation (19). The third equation of Equation (19) describes the linear electrical link between the voltage vectors on PV-buses ($\Delta {\mathit{V}}_{\mathit{g}}$,$\Delta {\mathbf{\theta}}_{\mathit{g}}$) as well as power angles in PV-buses ($\Delta {\mathbf{\delta}}_{\mathit{g}}$) with the generated power in these buses ($\Delta {\mathit{P}}_{\mathit{e}}$). This linear link has been created by constant matrix ${\mathit{K}}_{\mathbf{1}}$ to ${\mathit{K}}_{\mathbf{3}}$ expressed in Equation (20) to Equation (22). Considering Equation (17), the third equation of Equation (19) can be rewritten as Equation (23) to have a direct link between $\Delta {\mathbf{\delta}}_{\mathit{g}}$ and $\Delta {\mathit{P}}_{\mathit{e}}$.$$\{\begin{array}{c}{P}_{ei}=Re\left({S}_{i}\right)=\frac{{E}_{i}{V}_{i}}{{x}_{di}^{\text{'}}}sin\left({\delta}_{i}-{\theta}_{i}\right)\\ \Delta {\mathit{P}}_{\mathit{e}}={\displaystyle \sum _{i=1}^{m}}\left(\frac{\partial {P}_{ei}}{\Delta {\delta}_{i}}\Delta {\mathbf{\delta}}_{\mathit{i}}+\frac{\partial {P}_{ei}}{\partial {\theta}_{i}}\Delta {\mathbf{\theta}}_{\mathit{i}}+\frac{\partial {P}_{ei}}{\partial {V}_{i}}\Delta {\mathit{V}}_{\mathit{i}}\right)\\ \Delta {\mathit{P}}_{\mathit{e}}={\mathit{K}}_{\mathbf{1}}\Delta {\mathbf{\delta}}_{\mathit{g}}+{\mathit{K}}_{\mathbf{2}}\Delta {\mathbf{\theta}}_{\mathit{g}}+{\mathit{K}}_{\mathbf{3}}\Delta {\mathit{V}}_{\mathit{g}}\end{array}$$$$\{\begin{array}{c}{\mathit{K}}_{\mathbf{1}}=diag\left({k}_{11},{k}_{12},\dots \dots {k}_{1m}\right)\\ {k}_{1i}={\frac{\partial {P}_{ei}}{\partial {\delta}_{i}}|}_{{\theta}_{i},{V}_{i}=cte}=\frac{{E}_{i}{V}_{i}}{{x}_{di}^{\prime}}cos\left({\delta}_{i}-{\theta}_{i}\right)\end{array}$$$$\{\begin{array}{c}{\mathit{K}}_{\mathbf{2}}=diag\left({k}_{21},{k}_{22},\dots \dots {k}_{2m}\right)\\ {k}_{2i}={\frac{\partial {P}_{ei}}{\partial {\theta}_{i}}|}_{{\delta}_{i},{V}_{i}=cte}=-\frac{{E}_{i}{V}_{i}}{{x}_{di}^{\prime}}cos\left({\delta}_{i}-{\theta}_{i}\right)\end{array}$$$$\{\begin{array}{c}{\mathit{K}}_{\mathbf{3}}=diag\left({k}_{31},{k}_{32},\dots \dots {k}_{3m}\right)\\ {k}_{3i}={\frac{\partial {P}_{ei}}{\partial {V}_{i}}|}_{{\delta}_{i},{\theta}_{i}=cte}=\frac{{E}_{i}}{{x}_{di}^{\prime}}sin\left({\delta}_{i}-{\theta}_{i}\right)\end{array}$$$$\Delta {\mathit{P}}_{\mathit{e}}=\left({\mathit{K}}_{\mathbf{1}}+{\mathit{K}}_{\mathbf{2}}{\mathit{C}}_{\mathbf{2}}+{\mathit{K}}_{\mathbf{3}}{\mathit{A}}_{\mathbf{2}}\right)\Delta {\mathbf{\delta}}_{\mathit{g}}$$
- (ii)
- The second sub-group of equations creates the link between electrical characteristics and mechanical performance of the generation units as expressed in Equations (24) and (25). Based on these equations, the electromechanical couplings would be formed for the whole power system.$$\{\begin{array}{c}\frac{2{H}_{i}}{{\omega}_{s}}\frac{d\Delta {\omega}_{i}}{dt}=-\Delta {P}_{ei}-{D}_{i}\Delta {\omega}_{i}\\ \frac{2}{{\omega}_{s}}{\mathit{H}}_{\mathit{M}}\frac{d}{dt}\Delta {\mathbf{\omega}}_{\mathit{g}}=-\Delta {\mathit{P}}_{\mathit{e}}-{\mathit{D}}_{\mathit{M}}\Delta {\mathbf{\omega}}_{\mathit{g}}\end{array}$$

## 5. Modal Analysis of IEEE-14B Test System in Presence of RSSG-SPC

## 6. Detailed Time Domain Modelling

- (i)
- The results of dynamic analysis have been validated and the proposed method gives a trustable design of RSSG-SPC.
- (ii)
- A well-designed RSSG-SPC based on the suggested method can damp the electromechanical oscillations in active power and frequency which results in a significant improvement in the support to the dynamics of external power grid.

## 7. Real Time Laboratory Test

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Shen, W.; Chen, X.; Qiu, J.; Hayward, J.A.; Sayeef, S.; Osman, P.; Meng, K.; Dong, Z.Y. A comprehensive review of variable renewable energy levelized cost of electricity. Renew. Sustain. Energy Rev.
**2020**, 133, 1–14. [Google Scholar] [CrossRef] - Li, J.; Chen, S.; Wu, Y.; Wang, Q.; Liu, X.; Qi, L.; Lu, X.; Gao, L. How to make better use of intermittent and variable energy? A review of wind and photovoltaic power consumption in China. Renew. Sustain. Energy Rev.
**2021**, 137, 1–15. [Google Scholar] [CrossRef] - Hu, J.; Harmsen, R.; Crijns-Graus, W.; Worrell, E.; Broek, M.V.D. Identifying barriers to large-scale integration of variable renewable electricity into the electricity market: A literature review of market design. Renew. Sustain. Energy Rev.
**2018**, 81, 2181–2195. [Google Scholar] [CrossRef] - Kroposki, B.; Johnson, B.; Zhang, Y.; Gevorgian, V.; Denholm, P.; Hodge, B.M.; Hannegan, B. Achieving a 100% Renewable Grid: Operating Electric Power Systems with Extremely High Levels of Variable Renewable Energy. IEEE Power Energy Mag.
**2017**, 15, 61–73. [Google Scholar] [CrossRef] - Ahmed, S.D.; Al-Ismail, F.S.M.; Shafiullah, M.; Al-Sulaiman, F.A.; El-Amin, I.M. Grid Integration Challenges of Wind Energy: A Review. IEEE Access
**2020**, 8, 10857–10878. [Google Scholar] [CrossRef] - Wu, Y.; Chang, S.; Mandal, P. Grid-Connected Wind Power Plants: A Survey on the Integration Requirements in Modern Grid Codes. IEEE Trans. Ind. Appl.
**2019**, 55, 5584–5593. [Google Scholar] [CrossRef] - Guillamon, A.F.; Lázaro, E.G.; Muljadi, E.; García, A.M. Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time. Renew. Sustain. Energy Rev.
**2019**, 115, 1–12. [Google Scholar] - Mahmud, N.; Zahedi, A. Review of control strategies for voltage regulation of the smart distribution network with high penetration of renewable distributed generation. Renew. Sustain. Energy Rev.
**2016**, 64, 582–595. [Google Scholar] [CrossRef] - Remon, D.; Cañizares, C.A.; Rodriguez, P. Impact of 100-MW-scale PV plants with synchronous power controllers on power system stability in northern Chile. IET Gener. Transm. Distrib.
**2017**, 11, 2958–2964. [Google Scholar] [CrossRef] [Green Version] - Bevrani, H.; Ise, T.; Miura, Y. Virtual synchronous generators: A survey and new perspectives. Electr. Power Energy Syst.
**2014**, 54, 244–254. [Google Scholar] [CrossRef] - Serban, E.; Ordonez, M.; Pondiche, C. Voltage and Frequency Grid Support Strategies Beyond Standards. IEEE Trans. Power Electron.
**2017**, 32, 298–309. [Google Scholar] [CrossRef] - Beck, H.P.; Hesse, R. Virtual Synchronous Machine. In Proceedings of the 9th International Conference on Electrical Power Quality and Utilisation, Barcelona, Spain, 9–11 October 2007. [Google Scholar]
- Chen, Y.; Hasse, R.; Turschner, D.; Beck, H.P. Comparison of methods for implementing virtual synchronous machine on inverters. In Proceedings of the International Conference on Renewable Energies and Power Quality ICREPQ’12, Santiago de Compostela, Spain, 28–30 March 2012. [Google Scholar]
- Suul, J.A.; D’Arco, S.; Guidi, G. Virtual Synchronous Machine-Based Control of a Single-Phase Bi-Directional Battery Charger for Providing Vehicle-to-Grid Services. IEEE Trans. Ind. Appl.
**2016**, 52, 3234–3244. [Google Scholar] [CrossRef] - Zhong, Q.C.; Weiss, G. Synchronverters: Inverters That Mimic Synchronous Generators. IEEE Trans. Ind. Electron.
**2011**, 58, 1259–1267. [Google Scholar] [CrossRef] - Zhong, Q.C.; Hornik, T. Control of Power Inverters in Renewable Energy and Smart Grid Integration; John Willy: Hoboken, NJ, USA, 2013. [Google Scholar]
- Wang, X.; Taul, M.G.; Wu, H.; Liao, Y.; Blaabjerg, F.; Harnefors, L. Grid-Synchronization Stability of Converter-Based Resources—An Overview. IEEE Open J. Ind. Appl.
**2020**, 1, 115–134. [Google Scholar] [CrossRef] - Harnefors, L.; Johansson, N.; Zhang, L. Impact on Interarea Modes of Fast HVDC Primary Frequency Control. IEEE Trans. Power Syst.
**2017**, 32, 1350–1358. [Google Scholar] - Fang, J.; Tang, Y.; Li, H.; Li, X. A Battery/Ultracapacitor Hybrid Energy Storage System for Implementing the Power Management of Virtual Synchronous Generators. IEEE Trans. Power Electron.
**2018**, 33, 2820–2824. [Google Scholar] [CrossRef] - Wang, L.; Vo, Q.S.; Prokhorov, A.V. Stability Improvement of a Multimachine Power System Connected with a Large-Scale Hybrid Wind-Photovoltaic Farm Using a Supercapacitor. IEEE Trans. Ind. Appl.
**2018**, 54, 50–60. [Google Scholar] [CrossRef] - Rodriguez, P.; Candela, J.I.; Luna, A. Control of PV generation systems using the synchronous power controller. In Proceedings of the IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, 15–19 September2013; pp. 993–998. [Google Scholar]
- Elsaharty, M.A.; Luna, A.; Candela, J.I.; Rodriguez, P. A Unified Power Flow Controller Using a Power Electronics Integrated Transformer. IEEE Trans. Power Deliv.
**2019**, 34, 828–839. [Google Scholar] [CrossRef] [Green Version] - Rocabert, J.; Capó-Misut, R.; Muñoz-Aguilar, R.S.; Candela, J.I.; Rodriguez, P. Control of Energy Storage System Integrating Electrochemical Batteries and Supercapacitors for Grid-Connected Applications. IEEE Trans. Ind. Appl.
**2019**, 55, 1853–1862. [Google Scholar] [CrossRef] - Zhang, W.; Tarraso, A.; Rocabert, J.; Luna, A.; Candela, J.I.; Rodriguez, P. Frequency Support Properties of the Synchronous Power Control for Grid-Connected Converters. IEEE Trans. Ind. Appl.
**2019**, 55, 5178–5189. [Google Scholar] [CrossRef] - Rakhshani, E.; Remon, D.; Cantarellas, A.M.; Garcia, J.M.; Rodriguez, P. Virtual Synchronous Power Strategy for Multiple HVDC Interconnections of Multi-Area AGC Power Systems. IEEE Trans. Power Syst.
**2017**, 32, 1665–1677. [Google Scholar] [CrossRef] - Remon, D.; Cantarellas, A.M.; Mauricio, J.M.; Rodriguez, P. Power system stability analysis under increasing penetration of photovoltaic power plants with synchronous power controllers. IET Renew. Power Gener.
**2017**, 11, 733–741. [Google Scholar] [CrossRef] [Green Version] - Abdollahi, M.; Candela, J.I.; Rocabert, J.; Aguilar, R.S.M.; Hermoso, J.R. Synchronous power controller merits for dynamic stability improvement in long line by renewables. In Proceedings of the IEEE International Conference on Renewable Energy Research and Applications (ICRERA), Birmingham, UK; 2016; pp. 760–765. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Munoz-Aguilar, R.S.; Hermoso, J.R. Improving long line stability by integrating renewables using static synchronous generators. In Proceedings of the IEEE International Conference on Renewable Energy Research and Applications (ICRERA), Birmingham, UK, 20–23 November 2016; pp. 512–517. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Aguilar, R.S.M.; Rodriguez, P. Generation frequency support by renewable SSG SPC unit on interconnected areas. In Proceedings of the IEEE 6th International Conference on Renewable Energy Research and Applications (ICRERA), San Diego, CA, USA, 5–8 November 2017; pp. 977–982. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Aguilar, R.S.M.; Hermoso, J.R. Phase stability enhancement in big power networks using renewable generation units controlled by SPC. In Proceedings of the IEEE Energy Conversion Congress and Exposition (ECCE), Cincinnati, OH, USA, 1–5 October 2017; pp. 3266–3273. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Munoz-Aguilar, R.S.; Hermoso, J.R. Supporting Phase Stability on Interconnected Grids by Synchronous Renewable Virtual Power Plants. In Proceedings of the 43nd Annual Conference of the IEEE Industrial Electronics Society (IECON), Beijing, China, 29 October–1 November 2017; pp. 446–452. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Elsaharty, M.A. Active Power Limiter for Static Synchronous Generators in Renewable Applications. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**. [Google Scholar] [CrossRef] - Kundur, P. Power System Stability and Control; McGrawHill Education: New York, NY, USA, 1994. [Google Scholar]
- Anderson, P.M.; Fouad, A.A. Power System Control and Stability, 2nd ed.; Wiley-IEEE Press: New York, NY, USA, 2002. [Google Scholar]
- Abdollahi, M.; Candela, J.I.; Rocabert, J.; Elsaharty, M.A.; Rodriguez, P. Novel Analytical Method for Dynamic Design of Renewable SSG SPC Unit to Mitigate Low-Frequency Electromechanical Oscillations. IEEE Trans. Power Electron.
**2020**, 35, 7532–7544. [Google Scholar] [CrossRef]

**Figure 1.**Grid connection of Renewable Static Synchronous Generators controlled by Synchronous Power Controller (RSSG-SPC).

**Figure 8.**Two degrees of dynamic flexibility in RSSG-SPC. (

**a**) damping ratio of internal mode, (

**b**) frequency of internal modes.

$\mathit{\lambda}$ | Eigenvalues | $\mathit{f}\left(\mathbf{H}\mathbf{z}\right)$ | $\mathit{\xi}$ | Dominant States | Description |
---|---|---|---|---|---|

${\lambda}_{1,2}$ | $-2.8357$ | $-$ | $1.00$ | $-$ | $-$ |

${\lambda}_{3,4}$ | $-0.00\pm 13.3741i$ | $2.1286$ | $0.00$ | $\Delta {\delta}_{2},\text{}\Delta {\omega}_{2}$ | mode of SG_{2} |

${\lambda}_{5,6}$ | $0.00\pm 9.3868i$ | $1.4940$ | $0.00$ | $\Delta {\delta}_{5},\text{}\Delta {\omega}_{5}$ | mode of SG_{5} |

${\lambda}_{7,8}$ | $0.00\pm 11.3015i$ | $1.7987$ | $0.00$ | $\Delta {\delta}_{3:4},\text{}\Delta {\omega}_{3:4}$ | greatest impact: SG_{3} |

${\lambda}_{9,10}$ | $0.00\pm 10.9488i$ | $1.7426$ | $0.00$ | $\Delta {\delta}_{4:5},\text{}\Delta {\omega}_{4:5}$ | greatest impact: SG_{4} |

$\mathit{\lambda}$ | Eigenvalues | $\mathit{f}\left(\mathbf{H}\mathbf{z}\right)$ | $\mathit{\xi}$ |
---|---|---|---|

${\lambda}_{1,2}$ | $-8.0530$ | $-$ | $1.0000$ |

${\lambda}_{3,4}$ | $-6.0214\pm 8.1033i$ | $1.2897$ | $0.5964$ |

${\lambda}_{5,6}$ | $-0.0937\pm 9.5090i$ | $1.5134$ | $0.0099$ |

${\lambda}_{7,8}$ | $-0.0040\pm 11.3128i$ | $1.8005$ | $0.0004$ |

${\lambda}_{9,10}$ | $-0.0000\pm 10.9488i$ | $1.7426$ | $0.0000$ |

Grid | ||
---|---|---|

IEEE—14 Bus Standard Test System [30] Emulated RSSG-SPC in OPAL: $147\text{}\mathrm{MVA}$ | ||

Platform | ||

${S}_{N}$ | Rated apparent power | $5\text{}\mathrm{kVA}$ |

${V}_{ac}$ | Phase to phase grid voltage | $400\text{}\mathrm{V}$ |

${V}_{dc}$ | DC-link voltage | $600\text{}\mathrm{V}$ |

${L}_{T\left(abc\right)}$ | Coupling Transformer | $2\text{}\mathrm{mH}$ |

${L}_{f\left(abc\right)}$ | Filter Inductor | $6\text{}\mathrm{mH}$ |

${C}_{f\left(abc\right)}$ | Filter capacitor | $5\text{}\mathsf{\mu}\mathrm{F}$ |

${R}_{d\left(abc\right)}$ | Damping resistor | $1.8\text{}\mathrm{m}\mathsf{\Omega}$ |

${f}_{sw}$ | Switching frequency | $10\text{}\mathrm{kHz}$ |

RSSG-SPC | ||

${S}_{b}$ | Base power | $100\text{}\mathrm{MVA}$ |

${H}_{SSG}$ | Virtual inertia | $4.31\text{}\mathrm{s}$ |

${D}_{SSG}$ | Virtual damping | $0.51\text{}\mathrm{pu}$ |

${R}_{v}$ | Resistance of virtual admittance | $0.068\text{}\mathrm{pu}$ |

${X}_{v}$ | Reactance of virtual admittance | $0.20\text{}\mathrm{pu}$ |

${K}_{P}^{cc}$ | Proportional gain of current controller | $0.65$ |

${K}_{R}^{cc}$ | Resonant gain of current controller | $1.00$ |

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**MDPI and ACS Style**

Abdollahi, M.; Candela, J.I.; Tarraso, A.; Elsaharty, M.A.; Rakhshani, E.
Electromechanical Design of Synchronous Power Controller in Grid Integration of Renewable Power Converters to Support Dynamic Stability. *Energies* **2021**, *14*, 2115.
https://doi.org/10.3390/en14082115

**AMA Style**

Abdollahi M, Candela JI, Tarraso A, Elsaharty MA, Rakhshani E.
Electromechanical Design of Synchronous Power Controller in Grid Integration of Renewable Power Converters to Support Dynamic Stability. *Energies*. 2021; 14(8):2115.
https://doi.org/10.3390/en14082115

**Chicago/Turabian Style**

Abdollahi, Mostafa, Jose Ignacio Candela, Andres Tarraso, Mohamed Atef Elsaharty, and Elyas Rakhshani.
2021. "Electromechanical Design of Synchronous Power Controller in Grid Integration of Renewable Power Converters to Support Dynamic Stability" *Energies* 14, no. 8: 2115.
https://doi.org/10.3390/en14082115