# A Co-Simulation Framework for Power System Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. EMT Co-Simulation Framework

#### 2.1. Network Partitioning

#### 2.2. Interfacing

#### 2.3. Time-Step Delay Error

_{bci}(n) term in Equation (9) represents the i

_{th}interface value, which is exchanged between the subsystems. The errors which result from the delay in one subsystem would influence the simulation result of the other subsystem:

#### 2.4. Data Prediction by Extrapolation

_{i}range outside the known values. However, the interval should be kept as small as possible to maintain the estimation quality.

^{2}). As expressed in Equation (11), linear extrapolation assumes that the future data y

_{k +}

_{1}are on the line which passes two adjacent past data y

_{k}

_{−}

_{1}and y

_{k}. The algorithm is straightforward, and the computational load is minimal. However, the assumption can fail with high frequency signal components in the EMT simulation; thus, the integration time-step should be limited to be short enough to maintain the accuracy of the co-simulation. This process results in the increase in the total number of computations and thus the computational load:

^{4}), can reduce the interval to 13% compared with the linear method at the same level of summation of squared error (SSE).

_{k}(x) can be arranged as a tridiagonal system which is easy to solve to obtain the polynomial coefficients:

#### 2.5. Discontinuity Detection

_{i}, which is one of the equations for determining the spline polynomial coefficients, is compared with the heuristically determined threshold value to detect discontinuities. Discontinuity detection basically uses the slope of two successive data points thus magnitude, frequency and size of the computational time-step affect the threshold. k

_{p}is a heuristically determined constant which is generally in between 0.05 and 0.1 in 60 Hz system:

## 3. Case Study

#### 3.1. AC/DC Power System

#### 3.2. AC Distribution System

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CPU | Central processing unit |

DD | Discontinuity detection |

EMT | Electromagnetic transient |

FDNE | Frequency dependent network equivalent |

GUI | Graphical user interface |

HVDC | High voltage direct current transmission |

IPC | Interprocess communication |

R-L-C | Resistor, Inductor and Capacitor |

SSE | Sum squared error |

## References

- Chowdhury, S.P.; Chowdhury, S.; Crossley, P.A. UK scenario of islanded operation of active distribution networks with renewable distributed generators. Int. J. Electr. Power Energy Syst.
**2011**, 33, 1251–1255. [Google Scholar] [CrossRef] - Dommel, H.W.; Meyer, W.S. Computation of electromagnetic transients. Proc. IEEE
**1974**, 62, 983–993. [Google Scholar] [CrossRef] - Dommel, H.W. EMTP Theory Book; Bonneville Power Admin: Portland, OR, USA, 1986. [Google Scholar]
- Heffernan, M.D.; Turner, K.S.; Arrillaga, J.; Arnold, C.P. Computation of AC-DC System Disturbances—Part I. Interactive Coordination of Generator and Convertor Transient Models. IEEE Trans. Power Syst.
**1981**, 11, 4341–4348. [Google Scholar] [CrossRef] - Gao, F.; Kai, S. Multi-scale simulation of multi-machine power systems. Int. J. Electr. Power Energy Syst.
**2009**, 31, 538–545. [Google Scholar] [CrossRef] - Su, H.T.; Snider, L.A.; Chung, T.S.; Fang, D.Z. Recent advancements in electromagnetic and electromechanical hybrid simulation. In Proceedings of the International Conference on Power System Technology, Singapore, 21–24 November 2004; pp. 1479–1484.
- Lefebvre, S.; Mahseredjan, J. Interfacing Techniques for Transient Stability and Electromagnetic Transient Programs. IEEE Trans. Power Deliv.
**2009**, 24, 2385–2395. [Google Scholar] - Hui, S.Y.R.; Fung, K.K.; Christopoulos, C. Decoupled simulation of DC-linked power electronic systems using transmission-line links. IEEE Trans. Power Electron.
**1994**, 9, 85–91. [Google Scholar] [CrossRef] - Chiocchio, T.; Leonard, R.; Work, Y.; Fang, R.; Steurer, M.; Monti, A.; Khan, J.; Ordonez, J.; Sloderbeck, M.; Woodruff, S.L. A co-simulation approach for real-time transient analysis of electro-thermal system interactions on board of future all-electric ships. In Proceedings of the 2007 Summer Computer Simulation Conference, San Diego, CA, USA, 16 July 2007.
- Cécile, J.F.; Schoen, L.; Lapointe, V.; Abreu, A.; Bélanger, J. A Distributed Real-Time Framework for Dynamic Management of Heterogeneous Co-Simulations. Available online: http://www.rtlab.com/files/scs_article.pdf (accessed on 16 October 2015).
- Tylavsky, D.J.; Bose, A.; Alvarado, F.; Betancourt, R.; Clements, K.; Heydt, G.T.; Huang, G.; Ilic, M.; La Scala, M.; Pai, M.A. Parallel Processing in Power Systems Computation. IEEE Trans. Power Syst.
**1992**, 7, 629–638. [Google Scholar] - Tomin, M.A.; De Rybel, T.; Marti, J.R. Extending the Multi-Area Thévenin Equivalents method for parallel solutions of bulk power systems. Int. J. Electr. Power Energy Syst.
**2013**, 44, 192–201. [Google Scholar] [CrossRef] - Su, H.T.; Chan, K.W.; Snider, L.A. Parallel interaction protocol for electromagnetic and electromechanical hybrid simulation. IEEE Proc. Gener. Trans. Distrib.
**2005**, 152, 406–414. [Google Scholar] [CrossRef] - Marti, J.R.; Linares, L.R.; Calvino, J.; Dommel, H.W.; Lin, J. OVNI: An object approach to real-time power system simulators. In Proceedings of the International Conference on Power System Technology, Beijing, China, 18–21 August 1998; pp. 977–981.
- Sultan, M.; Reeve, J.; Adapa, R. Combined transient and dynamic analysis of HVDC and FACTS systems. IEEE Trans. Power Deliv.
**1998**, 13, 1271–1277. [Google Scholar] [CrossRef] - Wang, Y.P.; Watson, N.R. A benchmark test system for testing frequency dependent network equivalents for electromagnetic simulations. Int. J. Electr. Power Energy Syst.
**2013**, 44, 364–374. [Google Scholar] [CrossRef] - Annakkage, U.D.; Nair, N.-K.C.; Gole, A.M.; Dinavahi, V.; Noda, T.; Hassan, G.; Monti, A. Dynamic system equivalents: A survey of available techniques. IEEE Trans. Power Deliv.
**2009**, 27, 411–420. [Google Scholar] [CrossRef] - Gustavsen, B.; Semlyen, A. Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Deliv.
**1999**, 14, 1052–1061. [Google Scholar] [CrossRef] - Gustavsen, B.; Mo, O. Interfacing convolution based linear models to an electromagnetic transients program. Int. Conf. Power Syst. Trans.
**2007**, 1, 4–7. [Google Scholar] - Zhu, W.; Pekarek, S.; Jatskevich, J.; Wasynczuk, O.; Delisle, D. A Model-in-the-Loop Interface to Emulate Source Dynamics in a Zonal DC Distribution System. IEEE Trans. Power Electron.
**2005**, 20, 438–445. [Google Scholar] [CrossRef] - Wu, X.; Lentijo, S.; Deshmuk, A.; Monti, A.; Ponci, F. Design and implementation of a power-hardware-in-the-loop interface: A nonlinear load case study. In Proceedings of IEEE Applied Power Electronics Conference and Exposition, Austin, TX, USA, 6–10 March 2005; Volume 2, pp. 1332–1338.
- Ren, W.; Steurer, M.; Woodruff, S.; Andrus, M. Demonstrating the Power Hardware-in-the-Loop through Simulation of a Notional Destroyer-Class AllElectric Ship System during Crashback. In Proceedings of the ASNE Advanced Propulsion Symposium, Arlington, VA, USA, 30 October 2006.
- Noda, T.; Sasaki, S. Algorithms for distributed computation of electromagnetic transients toward pc cluster based real-time simulations. In Proceedings of the International Conference on Power System Transients, New Orleans, LA, USA, 28 September 2003.
- Dufour, C.; Paquin, J.-N.; Lapointe, V.; Be’langer, J.; Schoen, L. PC cluster-based real-time simulation of an 8-synchronous machine network with HVDC link using RT-LAB and TestDrive. In Proceedings of the 7th International Conference on Power Systems Transients, Lyon, France, 4–7 June 2007.
- Ren, W.; Steurer, M.; Woodruff, S. Accuracy evaluation in power hardware-in-the-loop (PHIL) simulation center for advanced power systems. In Proceedings of the 2007 Summer Computer Simulation Conference, San Diego, CA, USA, 16 July 2007.
- Fang, T.; Chengyan, Y.; Zhongxi, W.; Xiaoxin, Z. Realization of electromechanical transient and electromagnetic transient real time hybrid simulation in power system. In Proceedings of the IEEE/PES Transmission and Distribution Conference Exhibition, Dalian, China, 14 August 2005; pp. 1–6.
- Belanger, J.; Snider, L.A.; Paquien, J.; Pirolli, C.; Li, W. A Modern and Open Real-Time Digital Simulator of Contemporary Power Systems. In Proceedings of the International Conference on Power Systems Transients (IPST 2009), Kyoto, Japan, 2 June 2009; pp. 2–6.
- Jang, G.; Oh, S.; Hann, B.-M.; Kim, C.K. Novel reactive power compensation scheme for the Jeju-Haenam HVDC system. IEEE Proc. Gener. Trans. Distrib.
**2005**, 152, 514–520. [Google Scholar] [CrossRef] - Kersting, W.H. Radial distribution test feeders. In Proceedings of the 2001 Power Engineering Society Winter Meeting, Columbus, OH, USA, 31 January 2001; Volume 2, pp. 908–912.
- Jang, S.; Kim, K. An islanding detection method for distributed generations using voltage unbalance and total harmonic distortion of current. IEEE Trans. Power Deliv.
**2004**, 19, 745–752. [Google Scholar] [CrossRef] - Xin, H.; Qu, Z.; John, S.; Ali, M. A Self-Organizing Strategy for Power Flow Control of Photovoltaic Generators in a Distribution Network. IEEE Trans. Power Deliv.
**2011**, 26, 1462–1473. [Google Scholar] [CrossRef]

**Figure 11.**The effect of the compensation on (

**a**) the voltage and (

**b**) the high voltage direct current (HVDC) power.

**Figure 14.**Three-phase ground fault simulation using (

**a**) proposed framework and (

**b**) conventional simulation.

Specifications | HVDC System | AC System |
---|---|---|

Type | Line commutated converter | |

Rate Voltage | DC ±180 kV | 154 kV |

Rate Current | 849 A | - |

Rating | 300 MW | 75 MVA synchronous generator |

Number of circuits | 2 | - |

Converter Transformer | 3phase 3winding (YDY) | - |

Reactive power compensation | 70 MVA synchronous condensers | - |

Harmonic Filter | DTF 27.5 MVA X 2 for 11, 13th harmonics HPF 27.5 MVA X 2 for 23, 25th harmonics | - |

Type | Radial |
---|---|

Total Number of Bus | 34 |

Frequency | 60 Hz |

Voltage | 24.9 kV |

Number of Loads | Spot: 6, Distributed: 19 |

Total Load | Active: 1769 kW, Reactive: 1044 kW |

Transformer | 24.9 kV/4.16 kV, D-Y, 500 kVA |

Voltage Regulator | Y-Y with OLTC |

Shunt Capacitor | 750 kVA |

Type | Conventional | Co-simulation | ||
---|---|---|---|---|

Case | Reference | Common time-step | ||

CPU | Single core (3.2 GHz) | Multi core (2.66 GHz) | Single core (3.2 GHz) | Multi core (2.66 GHz) |

Time-step | 10 μs | 10 μs | 10 μs | 10 μs |

Computation time * | 1 | 1.12 | 6.72 | 0.51 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Oh, S.; Chae, S.
A Co-Simulation Framework for Power System Analysis. *Energies* **2016**, *9*, 131.
https://doi.org/10.3390/en9030131

**AMA Style**

Oh S, Chae S.
A Co-Simulation Framework for Power System Analysis. *Energies*. 2016; 9(3):131.
https://doi.org/10.3390/en9030131

**Chicago/Turabian Style**

Oh, Seaseung, and Suyong Chae.
2016. "A Co-Simulation Framework for Power System Analysis" *Energies* 9, no. 3: 131.
https://doi.org/10.3390/en9030131