# A Fundamental Study on the Transient Stability of Power Systems with High Shares of Solar PV Plants

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## Abstract

**:**

## 1. Introduction

- Proposal of a method for the creation of a standard parameter set for representing a wide array of large-scale solar PV plants and aggregated solar PV plants from the perspective of the TSO.
- A qualitative assessment of the influence of solar PV plants on transient stability when represented with different modeling representations.
- Provision of a relationship to determine the influence of solar PV plants on the transient stability.

## 2. Methodology

#### 2.1. Generic Modeling of Solar PV Plants

- Large-scale solar PV plants
- (Aggregation of) Distributed solar PV plants

#### 2.2. Large-Scale PV Model

- REGC_A—Renewable Energy Generator/Converter Module
- REEC_B—Renewable Energy Electrical Control Module
- REPC_A—Renewable Electrical Plant Level Control Module

#### 2.3. DER_A Model

#### 2.4. Grid Connection Requirements

- Additional reactive current is provided when the voltage deviation at the terminals of the individual power-generating modules is either larger than 10% of the effective value or when a sudden change in the instantaneous voltage occurs of at least 5% of the peak value of the nominal voltage.
- The additional injected reactive current $\Delta $Ib is the difference of the reactive current during the fault and the reactive current before the fault and is proportional to the voltage deviation as indicated in Equation (1). A graphical representation of Equation (1) for the values 2 and 5 of k is shown in Figure 5. When the voltage deviation is within the limits of the deadband, no additional reactive current is injected by the solar PV plants; the assigned deadband values will be discussed subsequently.$$\Delta Ib=\frac{(U-{U}_{0})}{{U}_{N}}\times {I}_{N}\times k$$$\Delta Ib$ = additional reactive current injection$\frac{U-{U}_{0}}{{U}_{N}}$ = $\Delta U$ = relative voltage deviation in puU = voltage during fault${U}_{0}$ = voltage before the fault${U}_{N}$ = nominal voltage${I}_{N}$ = nominal currentk = slope for additional reactive current injection
- The range of k or Kqv (additional reactive current gain) shall be between 2 and 6, where the value of 2 is assigned for power park modules connected to a network with a nominal voltage lower than 66 kV and the value of 5 is assigned for power park modules connected to a network with a nominal voltage of 66 kV and higher.

#### 2.5. Generic Model Parameters

## 3. Simulation Results

#### 3.1. Tools Used

#### 3.2. TenneT Network Case Study

- Case 1—100% of SGs connected
- Case 2—64% of SGs connected
- Case 3—59% of SGs connected
- Case 4—17% of SGs connected

#### 3.3. Assessment Method and Definitions

- Representation of all solar PV plants with their respective dynamic models. This representation shall be referred to as All dynamic models.
- Representation of all solar PV plants with negative load. This representation shall be referred to as All negative load.
- Representation of the solar PV plants connected at the faulted bus with dynamic models while all others are represented by negative load. This representation shall be referred to as Dynamic local 1. A further elaboration of this representation is shown in Figure 9 (The underlying elements of the PV system have been omitted in the figure for simplicity purposes).
- Representation of solar PV plants connected to at the faulted bus and solar PV plants connected at a bus directly connected to the faulted bus are represented with dynamic models. All other solar PV plants are represented with negative load. This representation shall be referred to as Dynamic local 2. A further elaboration of this representation is provided in Figure 10.

- SG — Synchronous generator
- A-PV Type A — Aggregated solar PV plants of type A
- A-PV Type BCD1— Aggregated solar PV plants of type B, C, D1
- L-PV — Large-scale PV system
- A-Wind — Aggregated wind systems

#### 3.4. Transient Stability Analysis

- High SCC PV ratio—The first distinction which can be made is for a faulted bus which possesses a high SCC PV ratio, this entails that the amount of short-circuit contribution of solar PV plants is high relative to the total short-circuit current at the faulted bus. Such an example was presented when evaluating the bus at GT150-B. In this studied case, the solar PV plants affected the transient stability notably. Additionally, for higher SCC PV ratios as case 4, it was shown that the transient stability was affected the most for this case when removing the dynamic behavior of the solar PV plants as the SCC PV ratio was the highest.
- Low SCC PV ratio—The second distinction which can be made is for an area or faulted bus which possesses a low SCC PV ratio, meaning that the amount of short-circuit contribution of solar PV plants is low compared to the total short-circuit current at the faulted bus. Examples of cases with low SCC PV ratios are EBK150-A and HGLB110-B. For these cases it was shown that the low contribution to the total short-circuit current by the solar PV plants led to them having little to no influence on the transient stability.

#### 3.5. Improving Transient Stability

- Limiting operation region of synchronous generator
- Addition of reactive compensation devices
- Decreasing reactance between synchronous generator and faulted bus

- By replacing the line/cable from the synchronous generator to the faulted bus with a line/cable with lower reactance. This alternative is very costly and does not provide any direct benefits other than an improved robustness and transfer capacity of added line. However, since the line will be completely replaced, the replacing line/cable can yield a low reactance.
- By adding a parallel line from synchronous generator to the faulted such that the equivalent reactance is hence decreased. This alternative offers redundancy and the ability to spread the transfer over two lines. However, as the equivalent reactance is also a function of the existing line/cable, this poses a limitation for the decrease in equivalent reactance.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Parameter | Description | Unit | Value |
---|---|---|---|

Tg | Converter time constant | s | 0.005 |

Rrpwr | Low Voltage Power Logic (LVPL) ramp rate limit | pu | 10.0 |

Brkpt | LVPL characteristic voltage 2 | pu | 0.70 |

Zerox | LVPL characteristic voltage 1 | pu | 0.10 |

Lvpl1 | LVPL gain | pu | 0 |

Volim | Voltage limit for high voltage reactive current management | pu | 2 |

Lvpnt1 | High voltage point for low voltage active current management | pu | 0.8 |

Lvpnt0 | Low voltage point for low voltage active current management | pu | 0 |

Iolim | Current limit for high voltage reactive current management (specified as a negative value) | pu | −1.1 |

Tfltr | Voltage filter time constant for low voltage active current management | s | 0.01 |

Khv | Overvoltage compensation gain used in the high voltage reactive current | – | 0 |

Iqrmax | Upper limit on rate of change for reactive current | pu | 99.0 |

Iqrmin | Lower limit on rate of change for reactive current | pu | 99.0 |

Accel | acceleration factor (0 < Accel ≤ 1) | – | 1 |

Parameter | Description | Unit | Value |
---|---|---|---|

Vdip | Low voltage condition trigger voltage | pu | 0.90 |

Vup | High voltage condition trigger voltage | pu | 1.10 |

Trv | Voltage filter time constant | s | 0.01 |

dbd1 | Overvoltage deadband for reactive current injection | pu | −0.1 |

dbd2 | Undervoltage deadband for reactive current injection | pu | 0.1 |

Kqv | Reactive current injection gain | pu | 5 |

Iqh1 | Maximum reactive current injection | pu | 1 |

Iql1 | Minimum reactive current injection | pu | −1 |

Vref0 | User defined reference (if 0, model initialises it to initial terminal voltage) | pu | 0 |

Tp | Filter time constant for electrical power | s | 0.01 |

QMax | limit for reactive power regulator | pu | 0.6 |

QMin | limit for reactive power regulator | pu | −0.6 |

VMAX | Max. limit for voltage control | pu | 1.1 |

VMIN | Min. limit for voltage control | pu | 0.9 |

Kqp | Reactive power regulator proportional gain | pu | 10 |

Kqi | Reactive power regulator integral gain | pu | 0.1 |

Kvp | Voltage regulator proportional gain | pu | 0.1 |

Kvi | Voltage regulator integral gain | pu | 0 |

Tiq | Reactive current regulator time constant | s | 0.01 |

dPmax | (>0) Power reference max. ramp rate | pu/s | 10 |

dPmin | (<0) Power reference min. ramp rate | pu/s | −10 |

PMAX | Max. power limit | pu | 1 |

PMIN | Min. power limit | pu | 0 |

Imax | Maximum limit on total converter current | pu | 1.1 |

Tpord | Power filter time constant | s | 0.01 |

Parameter | Description | Unit | Value |
---|---|---|---|

Tfltr | Voltage or reactive power measurement filter time constant | s | 0.01 |

Kp | Reactive power PI control proportional gain | pu | 0.1 |

Ki | Reactive power PI control integral gain | pu | 0.15 |

Tft | Lead time constant | s | 0.05 |

Tfv | Lag time constant | s | 0 |

Vfrz | Voltage below which State s2 is frozen | pu | 0 |

Rc | Line drop compensation resistance | pu | 0 |

Xc | Line drop compensation reactance | pu | 0 |

Kc | Reactive current compensation gain | pu | 0.33 |

emax | upper limit on deadband output | pu | 1 |

emin | lower limit on deadband output | pu | −1 |

dbd1 | lower threshold for reactive power control deadband (≤0) | pu | −0.005 |

dbd2 | upper threshold for reactive power control deadband (≥0) | pu | 0.005 |

Qmax | Upper limit on output of V/Q-control | pu | 0.4 |

Qmin | Lower limit on output of V/Q-control | pu | −0.4 |

Kpg | Proportional gain for power control | pu | 0.04 |

Kig | Proportional gain for power control | pu | 0.08 |

Tp | Real power measurement filter time constant | s | 0.05 |

fdbd1 | Deadband for frequency control, lower threshold (≤0) | Hz | 0 |

fdbd2 | Deadband for frequency control, upper threshold (≥0) | Hz | 0 |

femax | frequency error upper limit | pu | 1 |

femin | frequency error lower limit | pu | −1 |

Pmax | upper limit on power reference | pu | 1 |

Pmin | lower limit on power reference | pu | 0 |

Tg | Power Controller lag time constant | s | 0.1 |

Ddn | droop for over-frequency conditions | pu | 20 |

Dup | droop for under-frequency conditions | pu | 0 |

Parameter | Description | Unit | Value |
---|---|---|---|

Trv | voltage measurement transducer time constant | s | 0.01 |

Trf | frequency measurement transducer time constant | s | 0.01 |

dbd1 | lower voltage deadband (≤0) | pu | −0.1 |

dbd2 | upper voltage deadband (≥) | pu | 0.1 |

Kqv | proportional voltage control gain | pu | [0 2 5] |

Vref0 | user specified voltage set-point | pu | 0 |

Tp | power measurement transducer time constant | s | 0.01 |

Tiq | Q-control time constant | s | 0.01 |

Ddn | reciprocal of droop for over-frequency conditions (<0) | pu | 20 |

Dup | reciprocal of droop for under-frequency conditions (>0) | pu | 0 |

fdbd1 | deadband for frequency control, lower threshold | Hz | 0 |

fdbd2 | deadband for frequency control, upper threshold | Hz | 0 |

femax | frequency error upper limit | Hz | 1 |

femin | frequency error lower limit | Hz | −1 |

PMAX | Maximum power limit | pu | 1 |

PMIN | Minimum power limit | pu | 0 |

dPmax | Power reference maximum ramp rate (>0) | pu/s | 99 |

dPmin | Power reference minimum ramp rate (<0) | pu/s | −99 |

Tpord | Power filter time constant | s | 0.01 |

Kpg | PI controller proportional gain | pu | 0.1 |

Kig | PI controller integral gain | pu | 10 |

Imax | Maximum converter current | pu | 1.1 |

vl0 | inverter voltage break-point for low voltage cut-out | pu | 0.7 |

vl1 | inverter voltage break-point for low voltage cut-out (vl1 ≥ vl0) | pu | 0.7 |

vh0 | inverter voltage break-point for high voltage cut-out | pu | 1.1 |

vh1 | inverter voltage break-point for high voltage cut-out (vh1 ≤ vh0) | pu | 1.1 |

tvl0 | low voltage cut-out timer corresponding to voltage vl0 | s | 0.2 |

tvl1 | low voltage cut-out timer corresponding to voltage vl1 | s | 0.2 |

tvh0 | high voltage cut-out timer corresponding to voltage vh0 | s | 2 |

tvh1 | high voltage cut-out timer corresponding to voltage vh1 | s | 2 |

Vrfrac | fraction of device that recovers after voltage comes back to within vl1 < V < vh1 (0 ≤ Vrfrac ≤ 1) | – | 1 |

fl | inverter frequency break-point for low frequency cut-out | Hz | 47.5 |

fh | inverter frequency break-point for high frequency cut-out | Hz | 51.5 |

tfl | low frequency cut-out timer corresponding to frequency fl | s | 2 |

tfh | high frequency cut-out timer corresponding to frequency fh | s | 2 |

Tg | current control time constant (to represent behavior of inner control loops) (>0) | s | 0.005 |

rrpwr | ramp rate for real power increase following a fault | pu/s | 10 |

Tv | time constant on the output of the multiplier | s | 0.01 |

Vpr | voltage below which frequency tripping is disabled | pu | 0.3 |

Iqhl | upper limit on reactive current injection | pu | 1 |

Iqll | lower limit on reactive current injection | pu | −1 |

## References

- Qin, D.; Manning, M.; Chen, Z.; Marquis, M.; Averyt, K.; Tignor, M.; Miller, H. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. In Climate Change 2007: The Physical Science Basis; Cambridge University Press: New York, NY, USA, 2007; pp. 12–17. [Google Scholar]
- NASA Team. Global Surface Temperature. 2019. Available online: https://climate.nasa.gov/vital-signs/global-temperature/ (accessed on 13 August 2020).
- Butler, C.D. Climate change, health and existential risks to civilization: A comprehensive review (1989–2013). Int. J. Environ. Res. Public Health
**2018**, 15, 2266. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ruyssenaars, P.; Coenen, P.; Zijlema, P.; Arets, E.; Baas, K.; Dröge, R.; Geilenkirchen, G.; T Hoen, M.; Honig, E.; Huet, B. Greenhouse Gas Emissions in the Netherlands 1990–2017: National Inventory Report 2019; National Institute for Public Health and the Environment: Bilthoven, The Netherlands, 2019; pp. 58–59.
- Akpan, U.; Akpan, G. The contribution of energy consumption to climate change: A feasible policy direction. Int. J. Energy Econ. Policy
**2011**, 2, 21–33. [Google Scholar] - United Nations. Paris Agreement. UNFCCC. 2015. Available online: https://unfccc.int/sites/default/files/english_paris_agreement.pdf (accessed on 12 August 2020).
- Klimaatakkoord. 2019. Available online: https://www.klimaatakkoord.nl/documenten/publicaties/2019/06/28/klimaatakkoord (accessed on 13 August 2020).
- Eguia, P.; Etxegarai, A.; Torres, E.; Martín, J.; Albizu, I. Use of generic dynamic models for photovoltaic plants. Renew. Energy Power Qual. J.
**2015**, 368–373. [Google Scholar] [CrossRef] - Yamashita, K.; Renner, H.; Martinez Villanueva, S.; Vennemann, K.; Martins, J.; Aristidou, P.; Van Cutsem, T.; Song, Z.; Lammert, G.; Pabon, L.; et al. Modelling of Inverter-Based Generation for Power System Dynamic Studies. 2018, Volume 298, pp. 81–87. Available online: http://cired.net/uploads/default/files/727-web.pdf (accessed on 17 August 2020).
- Lammert, G.; Yamashita, K.; Renner, H.; Martinez, S.; Pourbeik, P.; Ciausiu, F.; Pabon, L.; Braun, M. International industry practice on modelling and dynamic performance of inverter based generation in power system studies. CIGRE Sci. Eng.
**2017**, 8, 25–37. [Google Scholar] - Breithaupt, T.; Herwig, D.; Hofmann, L.; Mertens, A.; Meyer, R.; Farrokhseresht, N.; Tuinema, B.; Wang, D.; Rueda Torres, J.; Ruberg, S.; et al. Deliverable D1.1 Report on Systemic Issues; MIGRATE Project Consortium: Bayreuth, Germany, 2016; p. 137. [Google Scholar]
- Boemer, J.; Burges, K.; Nabe, C.; Pöller, M. All Island TSO Facilitation of Renewables Studies; Eirgrid: Dublin, Ireland, 2010. [Google Scholar]
- Oh, S.; Shin, H.; Cho, H.; Lee, B. Transient impact analysis of high renewable energy sources penetration according to the future korean power grid scenario. Sustainability
**2018**, 10, 4140. [Google Scholar] [CrossRef] [Green Version] - Mohamed, S.R.; Jeyanthy, P.A.; Devaraj, D. Investigation on the impact of high-penetration of PV generation on transient stability. In Proceedings of the 2017 IEEE International Conference on Intelligent Techniques in Control, Optimization and Signal Processing (INCOS), Srivilliputhur, India, 23–25 March 2017; pp. 1–6. [Google Scholar]
- Lammert, G. Modelling, Control and Stability Analysis of Photovoltaic Systems in Power System Dynamic Studies. Ph.D. Thesis, University of Kassel, Kassel, Germany, 2019. [Google Scholar]
- Göksu, Ö.; Sorensen, P.; Fortmann, J.; Morales, A.; Weigel, S.; Pourbeik, P. Compatibility of IEC 61400-27-1 Ed 1 and WECC 2nd Generation Wind Turbine Models. In Proceedings of the International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Power Plants, Vienna, Austria, 15–17 November 2016. [Google Scholar]
- Pourbeik, P.; Sanchez-Gasca, J.J.; Senthil, J.; Weber, J.D.; Zadehkhost, P.S.; Kazachkov, Y.; Tacke, S.; Wen, J.; Ellis, A. Generic dynamic models for modeling wind power plants and other renewable technologies in large-scale power system studies. IEEE Trans. Energy Convers.
**2017**, 32, 1108–1116. [Google Scholar] [CrossRef] - WECC Renewable Energy Modeling Task Force. Central Station PV Plant Model Validation Guideline. 2015. Available online: https://www.wecc.org/Reliability/Central%20Station%20Photovoltaic%20Power%20Plant%20Model%20Validation%20Guideline%20June%2017%202015.pdf (accessed on 24 August 2020).
- WECC Renewable Energy Modeling Task Force. Solar Photovoltaic Power Plant Modeling and Validation Guideline. 2019. Available online: https://www.wecc.org/Reliability/Solar%20PV%20Plant%20Modeling%20and%20Validation%20Guidline.pdf (accessed on 24 August 2020).
- Lammert, G.; Ospina, L.D.P.; Pourbeik, P.; Fetzer, D.; Braun, M. Implementation and validation of WECC generic photovoltaic system models in DIgSILENT PowerFactory. In Proceedings of the 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA, 17–21 July 2016; pp. 1–5. [Google Scholar] [CrossRef]
- Eguia, P.; Etxegarai, A.; Torres, E.; San Martin, J.I.; Albizu, I. Modeling and validation of photovoltaic plants using generic dynamic models. In Proceedings of the 2015 International Conference on Clean Electrical Power (ICCEP), Taormina, Italy, 16–18 June 2015; pp. 78–84. [Google Scholar] [CrossRef]
- Machlev, R.; Batushansky, Z.; Soni, S.; Chadliev, V.; Belikov, J.; Levron, Y. Verification of utility-scale solar photovoltaic plant models for dynamic studies of transmission networks. Energies
**2020**, 13, 3191. [Google Scholar] [CrossRef] - WECC Renewable Energy Modeling Task Force. Generic Solar Photovoltaic System Dynamic Simulation Model Specification; Sandia National Laboratories: Albuquerque, NM, USA; Livermore, CA, USA, 2012.
- Ramasubramanian, D.; Alvarez-Fernandez, I.; Mitra, P.; Gaikwad, A.; Boemer, J.C. The New Aggregated Distributed Energy Resources (der_a) Model for Transmission Planning Studies: 2019 Update; Electric Power Research Institure (EPRI): Washington, DC, USA, 2019. [Google Scholar]
- North American Electric Reliability Corporation (NERC). Reliability Guideline Parameterization of the DER_A Model; North American Electric Reliability Corporation (NERC): Atlanta, GA, USA, 2019. [Google Scholar]
- Elliott, R.T.; Ellis, A.; Pourbeik, P.; Sanchez-Gasca, J.J.; Senthil, J.; Weber, J. Generic photovoltaic system models for WECC—A status report. In Proceedings of the IEEE PES General Meeting, Denver, CO, USA, 26–30 July 2015; pp. 1–5. [Google Scholar] [CrossRef]
- WECC Renewable Energy Modeling Task Force. WECC Solar Plant Dynamic Modeling Guidelines. 2014. Available online: https://www.wecc.org/reliability/wecc%20solar%20plant%20dynamic%20modeling%20guidelines.pdf (accessed on 28 August 2020).
- Pourbeik, P.; Weber, J.; Ramasubramanian, D.; Sanchez-Gasca, J.; Senthil, J.; Zadkhast, P.; Boemer, J.; Gaikwad, A.; Green, I.; Tacke, S.; et al. An Aggregate Dynamic Model for Distributed Energy Resources for Power System Stability Studies. CIGRE Sci. Eng.
**2019**, 14, 38–48. [Google Scholar] - Boemer, J. On Stability of Sustainable Power Systems: Network Fault Response of Transmission Systems with Very High Penetration of Distributed Generation. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2016. [Google Scholar] [CrossRef]
- Commission Regulation (EU). Establishing a network code on requirements for grid connection of generators. Off. J. Eur. Union
**2016**, 112, 1–68. [Google Scholar] - De Autoriteit Consument en Markt. Netcode Elektriciteit. 2016. Available online: https://wetten.overheid.nl/BWBR0037940/2018-12-22 (accessed on 2 September 2020).
- Netbeheer Nederland. Netcode Elektriciteit met Onderhanden Zijnde Codewijzigingenvoorstellen. 2019. Available online: https://www.netbeheernederland.nl/_upload/Files/E02_-_Netcode_elektriciteit_112.pdf (accessed on 2 September 2020). (In Dutch).
- Lammert, G.; Premm, D.; Ospina, L.D.P.; Boemer, J.C.; Braun, M.; Van Cutsem, T. Control of photovoltaic systems for enhanced short-term voltage stability and recovery. IEEE Trans. Energy Convers.
**2019**, 34, 243–254. [Google Scholar] [CrossRef] [Green Version]

Generator Type | Voltage Level | Operator | Capacity Range |
---|---|---|---|

Type 0 | <110 kV | and | 0–0.0008 MW |

Type A | <110 kV | and | 0.0008 MW–1 MW |

Type B | <110 kV | and | 1 MW–50 MW |

Type C | <110 kV | and | 50 MW–60 MW |

Type D1 | <110 kV | and | ≥60 MW |

Type D2 | ≥110 kV | and | all |

Requirement | Type A | Type B | Type C | Type D |
---|---|---|---|---|

Fault-ride-through capability of generators connected below 110 kV | x | x | x | D1 |

Fault-ride-through capability of generators connected at 110 kV or above | x | x | x | D2 |

Provision of fast fault current (for IBG) | x | x | x | x |

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

Vdip* (pu) | Low voltage condition trigger voltage | 0.9 |

Vup* (pu) | High voltage condition trigger voltage | 1.1 |

dbd1 (pu) | Overvoltage deadband for reactive current injection | −0.1 |

dbd2 (pu) | Undervoltage deadband for reactive current injection | 0.1 |

Kqv | Reactive current injection gain | [2 5] |

Iqhl (pu) | Maximum reactive current injection | 1 |

Iqll (pu) | Minimum reactive current injection | −1 |

Representation | CCT Case 1 (ms) | CCT Case 2 (ms) | CCT Case 3 (ms) | CCT Case 4 (ms) |
---|---|---|---|---|

All dynamic models | 279 | 274 | 274 | 272 |

All negative load | 268 | 256 | 256 | 237 |

Dynamic local 1 | 270 | 256 | 261 | 242 |

Dynamic local 2 | 274 | 261 | 265 | 247 |

Case | SCC Case 1 (kA) | SCC Case 2 (kA) | SCC Case 3 (kA) | SCC Case 4 (kA) |
---|---|---|---|---|

Total SCC | 59.64 | 57.26 | 57.32 | 54.25 |

Total SCC PV | 9.09 | 9.38 | 9.46 | 9.97 |

SCC PV ratio | 15.25% | 16.37% | 16.50% | 18.37% |

Representation | CCT Case 1 (ms) | CCT Case 2 (ms) | CCT Case 3 (ms) | CCT Case 4 (ms) |
---|---|---|---|---|

All dynamic models | 272 | 268 | 270 | 270 |

All Negative load | 272 | 268 | 268 | 268 |

Dynamic local 1 | 272 | 268 | 268 | 268 |

Dynamic local 2 | 272 | 268 | 268 | 268 |

Case | SCC Case 1 (kA) | SCC Case 2 (kA) | SCC Case 3 (kA) | SCC Case 4 (kA) |
---|---|---|---|---|

Total SCC | 25.35 | 25.34 | 25.28 | 25.06 |

Total SCC PV | 2.46 | 2.48 | 2.51 | 2.61 |

SCC PV Ratio | 9.70% | 9.80% | 9.94% | 10.41% |

Representation | CCT Case 1 (ms) | CCT Case 2 (ms) | CCT Case 3 (ms) | CCT Case 4 (ms) |
---|---|---|---|---|

All dynamic models | 322 | 320 | 320 | 322 |

All negative load | 320 | 315 | 317 | 317 |

Dynamic local 1 | 320 | 315 | 317 | 317 |

Dynamic local 2 | 320 | 315 | 317 | 317 |

Case | SCC Case 1 (kA) | SCC Case 2 (kA) | SCC Case 3 (kA) | SCC Case 4 (kA) |
---|---|---|---|---|

Total SCC | 32.23 | 32.14 | 32.04 | 32.14 |

Total SCC PV | 2.53 | 2.59 | 2.63 | 2.70 |

SCC PV Ratio | 7.86% | 8.05% | 8.20% | 8.41% |

SG at Bus 87000 | P (MW) | Q (Mvar) | CCT (ms) |
---|---|---|---|

Operating Point 1 | 620 | 90.00 | 274 |

Operating Point 2 | 620 | 0.00 | 256 |

Operating Point 3 | 620 | −45.00 | 242 |

Operating Point 4 | 450 | 30.00 | 387 |

Operating Point 5 | 450 | −30.00 | 359 |

Operating Point 6 | 250 | 0 | >400 |

Case | CCT (ms) |
---|---|

Without SC | 268 |

With SC | 293 |

Case | X (pu) | CCT (ms) |
---|---|---|

Initial reactance | 0.001430 | 274 |

Modified reactance | 0.0004 | 279 |

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## Share and Cite

**MDPI and ACS Style**

Kalloe, N.; Bos, J.; Rueda Torres, J.; van der Meijden, M.; Palensky, P.
A Fundamental Study on the Transient Stability of Power Systems with High Shares of Solar PV Plants. *Electricity* **2020**, *1*, 62-86.
https://doi.org/10.3390/electricity1010005

**AMA Style**

Kalloe N, Bos J, Rueda Torres J, van der Meijden M, Palensky P.
A Fundamental Study on the Transient Stability of Power Systems with High Shares of Solar PV Plants. *Electricity*. 2020; 1(1):62-86.
https://doi.org/10.3390/electricity1010005

**Chicago/Turabian Style**

Kalloe, Nikhil, Jorrit Bos, Jose Rueda Torres, Mart van der Meijden, and Peter Palensky.
2020. "A Fundamental Study on the Transient Stability of Power Systems with High Shares of Solar PV Plants" *Electricity* 1, no. 1: 62-86.
https://doi.org/10.3390/electricity1010005