# Non-Intrusive Delay-Based Model Partitioning for Distributed Real-Time Simulation

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## Abstract

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## 1. Introduction

## 2. Literature Review and Related Work on System Partitioning

## 3. Motivation

#### 3.1. Distributed Real-Time Power System Simulations

#### 3.2. Simulation Examples Explaining Paper Motivation

## 4. Mathematical Background of Analysis and Methodology

#### 4.1. State-Space Representation of Partitioned System Model

#### 4.2. Modal Analysis

## 5. Analysis and Non-Intrusive Delay-Based System Partitioning

#### 5.1. Analysis

#### 5.2. Methodology

#### 5.2.1. Method and Analysis Exemplification

## 6. Testing of the Method on the Realistic Power System Model

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Response of ${x}_{1}$ in system example 1 after the disturbance—decoupling points A and B.

**Figure 10.**Time response of ${I}_{{L}_{inv}}$ for decoupling point R1 and monolithic system simulation.

Mode i | Value | ${\mathit{\zeta}}_{\mathit{i}}$ | ${\mathit{\omega}}_{\mathit{n},\mathit{i}}$ | ${{T}}_{{\mathit{i}}_{\mathit{cr}}\left[\mathbf{ms}\right]}$ |
---|---|---|---|---|

$mod{e}_{1}$ | −451.63 ± 904.73 · i | 0.44663 | 1011.2 | 0.62137 |

$mod{e}_{2}$ | −77.33 ± 146.50 · i | 0.46683 | 165.65 | 3.7931 |

$mod{e}_{3}$ | −140.91 | 1 | 140.91 | - |

$mod{e}_{4}$ | −101.18 | 1 | 101.18 | - |

Mode Value | ${\mathit{\zeta}}_{{i}}$ | ${\mathit{\omega}}_{\mathit{n},1}$ | |
---|---|---|---|

Monolithic model-continuous | −451.63 + 904.73 ·i | 0.447 | 1.01 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ |

Monolithic model-discrete | −451.27 + 904.51 ·i | 0.446 | 1.01 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ |

Decoupled model | −426.01 + 919.75 ·i | 0.420 | 1.01 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ |

$\mathit{d}=\mathbf{50}\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}{s}$ | −373.91 + 941.87 ·i | 0.369 | 1.01 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ |

$\mathit{d}=\mathbf{100}\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}{s}$ | −318.14 + 957.58 ·i | 0.315 | 1.01 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$ |

$\mathit{d}=\mathbf{150}\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}{s}$ | −262.99 + 963.08 ·i | 0.263 | 9.98 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{2}$ |

$\mathit{d}=\mathbf{250}\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}{s}$ | −162.27 + 952.21 ·i | 0.168 | 9.66 $\times \phantom{\rule{3.33333pt}{0ex}}{0}^{2}$ |

$\mathit{d}=\mathbf{500}\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}{s}$ | 184.81 + 859.60 · i | −0.21 | 8.79 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{2}$ |

Parameter | Value | Parameter | Value |
---|---|---|---|

${f}_{s}$ | 40 kHz | ${S}_{rated}$ | 8.5 kVA |

${L}_{inv}$ | 0.535 mH | ${V}_{LL}$ | 400 V |

${V}_{DC}$ | $700\phantom{\rule{3.33333pt}{0ex}}V$ | ${C}_{filter}$ | 9.3846 $\mathsf{\mu}$F |

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**MDPI and ACS Style**

Bogdanovic, M.; Stevic, M.; Monti, A.
Non-Intrusive Delay-Based Model Partitioning for Distributed Real-Time Simulation. *Energies* **2022**, *15*, 767.
https://doi.org/10.3390/en15030767

**AMA Style**

Bogdanovic M, Stevic M, Monti A.
Non-Intrusive Delay-Based Model Partitioning for Distributed Real-Time Simulation. *Energies*. 2022; 15(3):767.
https://doi.org/10.3390/en15030767

**Chicago/Turabian Style**

Bogdanovic, Milica, Marija Stevic, and Antonello Monti.
2022. "Non-Intrusive Delay-Based Model Partitioning for Distributed Real-Time Simulation" *Energies* 15, no. 3: 767.
https://doi.org/10.3390/en15030767