# Synchronous Generator Out of Step Detection Using Real Time Load Angle Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Analysis and selection of the load angle measurement method
- Development of the real time load angle measurement algorithm
- Development of the loss of synchronicity detection algorithm based on the real time load angle measurement

## 2. Power System Stability and Load Angle

#### 2.1. Power System Stability

_{g}is induced generator voltage, U

_{s}is voltage at generator terminals, X is generator reactance and δ is the angle between voltages or load angle. A graphical representation of this nonlinear equation is shown in Figure 1.

_{n}at the load angle of δ

_{n}. After the protection trip occurs and the breaker is opened, the transferred power is reduced instantaneously and the mechanical power remains the same. Due to this difference, the rotor starts to accelerate and the angle δ increases. When the fault is cleared, the reached angle is δ

_{C}but the rotor continues to accelerate since there is accumulated kinetic energy in it. At this point the rotor starts to decelerate since the electric torque is higher than the mechanical. The rotor decelerates till the angle δ

_{F}is reached and all accumulated kinetic energy is used up. In Figure 1 and Figure 2 it can be noticed that a critical angle δ

_{L}exists, above which further increase in the angle results in lower electrical power and the generator starts to accelerate with no recovery. It can be concluded that the generator will maintain its stability if there is sufficient decelerating energy to oppose the acceleration. This is called the equal area criterion.

#### 2.2. Load Angle Definition and Measurement

_{q}mathematical model of the synchronous generator. In this representation the load angle is defined as the electrical angle between the space vector of the excitation voltage ē

_{q}and the terminal voltage space vector $\overline{{v}_{t}}$. Since ē

_{q}lies along the positive q axis, the load angle can also be defined as the electrical angle between the q axis and the voltage vector $\overline{{v}_{t}}$. At no-load condition ē

_{q}and $\overline{{v}_{t}}$ are identical and the load angle equals zero.

_{δ}recorded at a constant rotor speed and a sketch of the air gap width configuration [12]. The signal u

_{δ1}is a fundamental component of the u

_{δ}signal and both signals are expressed in volts, while the angle $\vartheta $ is expressed in electrical radians. The load angle measurements require the air gap sensor signal to be tightly bound to the rotor position. If the rotor position correlates with the induced EMF, it can be used to determine the value of the load angle together with a terminal voltage signal. It can also be said that the phase shift of the capacitive air gap sensor signal towards the terminal voltage signal represents the load angle.

#### 2.3. Loss of Synchronicity Detection Methods

_{A}and Z

_{B}and the line impedance Z

_{L}, then the impedance characteristic is presented in Figure 9.

_{A}and E

_{B}are equal, i.e., E

_{A}/E

_{B}= 1 then the impedance characteristic is represented by the line PQ, and the angle between lines AP and BP is the load angle between the two systems δ. The line AB stands for total impedance. If system B is used as the reference system and it is assumed that E

_{A}is leading E

_{B}, then the impedance is changing from point A towards point B. During the loss of synchronicity, the impedance travels from point P to point Q. When the impedance intersects total impedance, the angle between two systems is 180° and it can be said that the systems are out of step. This point of intersection is known as the electrical center of the system. The impedance continues to travel and reaches again the point when the systems are in phase. At this point it is said that one out of step cycle has been completed. When the ratio E

_{A}/E

_{B}is not equal to 1, the impedance characteristics are represented by the curves as can be seen in Figure 9.

_{A}, line impedance Z

_{L}and system B with impedance Z

_{B}. The position of the loss of synchronicity protection relay is usually at the generator terminals and it divides total impedance into m⋅Z

_{tot}and (1 − m)⋅Z

_{tot}[21]. Impedance at the measurement location can be calculated by Equation (6):

- Single blinder scheme
- Double blinder scheme
- Lens scheme
- Two zones scheme with straight lines

_{0}is the rated angular velocity. P

_{m}and P

_{e}are the mechanical input power and electrical output power respectively, δ is the load angle and ω is generator angular speed. From the equations and from what is stated in this chapter it can be concluded that if the load angle would be measured in real time, it could be used for generator loss of synchronicity protection purposes.

## 3. Materials and Methods

#### 3.1. Real Time Load Angle Measurement Algorithm

#### 3.2. Testing Environment for Real Time Load Angle Measurement

#### 3.3. Loss of Synchronicity Simulation Model

## 4. Results

#### 4.1. Testing Results of the Real Time Load Angle Measurement Algorithm

#### 4.2. Loss of Synchronicity Simulation Results

_{L}will be passed and further increase in the load angle will result in lower electrical power and the generator will start to accelerate with no recovery.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Machowski, J.; Bialek, J.W.; Bumby, J.R. Power System Dynamics, Stability and Control; John Wiley & Sons Ltd.: New Jersey, NJ, USA, 2008. [Google Scholar]
- Abedini, M.; Davarpanah, M.; Sanaye-Pasand, M.; Hashemi, S.M.; Iravani, R. Generator Out-of-Step Prediction Based on Faster-Than Real Tine Analysis: Concepts and Applications. IEEE Trans. Power Syst.
**2018**, 33, 4563–4573. [Google Scholar] [CrossRef] - Berdy, J. Out of Step Protection for Generators; General Electric Power Management: Ontario, ON, Canada. Available online: https://store.gegridsolutions.com/FAQ/Documents/CEB/GER-3179.pdf (accessed on 26 April 2020).
- Cheng, S.; Sachdev, M.S. Out of Step Protection Using the Equal Area Criterion. In Proceedings of the 18th Annual Canadian Conference on Electrical and Computer Engineering, Saskatoon, SK, Canada, 1–4 May 2005; pp. 1488–1491. [Google Scholar]
- Reimert, D. Protective Relaying for Power Generation Systems; Taylor & Francis: Abingdon, UK, 2006. [Google Scholar]
- Jadrić, M.; Frančić, B. Dynamics of Electrical Machines; Graphis: Zagreb, Croatia, 1997. [Google Scholar]
- Mišković, M.; Mirošević, M.; Ergec, G. Load Angle Estimation of a Synchronous Generator Using Dynamical Neural Networks. J. Energy
**2009**, 58, 174–191. [Google Scholar] - Višić, I.; Strnad, I.; Tonković, T. Real Time Load Angle Application for Synchronous Generator Protection Purposes. J. Energy
**2020**, 69, 13–17. [Google Scholar] [CrossRef] - Viši#x107;, I.; Strnad, I.; Tonković, T. Real Time Load Angle Application for Synchronous Generator Protection Purposes. In Proceedings of the 2nd International Colloquium on Intelligent/Smart Grid Metrology 2019—SMAGRIMET, Split, Croatia, 9–12 April 2019; pp. 66–70. [Google Scholar]
- Kundur, P. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994. [Google Scholar]
- Tziouvaras, D.A.; Hou, D. Out-of-step protection fundamentals and advancements. In Proceedings of the 57th Annual Conference for Protective Relay Engineers, College Station, TX, USA, 1 April 2004; pp. 282–307. [Google Scholar]
- Despalatović, M.; Jadrić, M.; Terzić, B. Real-time power angle determination of salient-pole synchronous machine based on air gap measurements. Electr. Power Syst. Res.
**2008**, 78, 1873–1880. [Google Scholar] [CrossRef] - Veski Capacitive air Gap Sensor. Available online: https://www.veski.hr/index.php?page=sensors-ag (accessed on 30 May 2020).
- Vibrosystm Air Gap Monitoring. Available online: https://www.vibrosystm.com/en/product/vm_air_gap (accessed on 30 May 2020).
- Iris Power Capacitive Air Gap Sensor. Available online: https://irispower.com/products/capacitive-air-gap-sensor/ (accessed on 30 May 2020).
- Orešković, G.; Meško, B. HPP Dubrava—Power Swings and Electromechanical Oscillations of Generator A and B. Expert Study; Veski Ltd.; Faculty of Electrical Engineering and Computing: Zagreb, Croatia, 2004. [Google Scholar]
- Despalatović, M.; Jadrić, M.; Terzić, B.; Macan, J. On-Line Hydrogenerator Power Angle and Synchronous Reactances Determination Based on Air Gap Measurement. In Proceedings of the IEEE PES Power Systems Conference and Exposition, New York, NY, USA, 10–13 October 2004; pp. 753–758. [Google Scholar]
- Jadrić, M.; Despalatović, M.; Terzić, B.; Rajković, B. Methodology for Synchronous Hydrogenerator Parameter Identification Based on Monitoring System Measurement. Automatika
**2007**, 48, 9–19. [Google Scholar] - Lopac, N.; Bulic, N.; Vrkic, N. Sliding Mode Observer-Based Load Angle Estimation for Salient-Pole Wound Rotor Synchronous Generators. Energies
**2019**, 12, 1609. [Google Scholar] [CrossRef][Green Version] - International Guide on the protection of Synchronous Generators; CIGRE Working Group B5.04. Brochure
**2011**, 479, 122–133. - SIPROTEC 4 Generator Protection 7UM62 Manual; Siemens AG: Nürnberg, Germany, 2017.
- Fischer, N.; Benmouyal, G.; Hou, D.; Tziouvaras, D.; Byrne-Finley, J.; Smith, B. Tutorial on Power Swing Blocking and Out-of-Step Tripping. In Proceedings of the 39th Annual Western Protective Relay Conference, Spokane, WA, USA, 16–18 October 2012. [Google Scholar]
- Camarillo-Peñaranda, J.R.; Celeita, D.; Gutierrez, M.; Toro, M.; Ramos, G. An Approach for Out-of-Step Protection Based on Swing Center Voltage Estimation and Analytic Geometry Parameters. IEEE Trans. Ind. Appl.
**2020**, 56, 2402–2408. [Google Scholar] [CrossRef] - Redfern, M.A.; Checksfield, M.J. A New Pole Slip Protection Algorithm for Dispersed Storage and Generation using the Equal Area Criterion. IEEE Trans. Power Deliv.
**1995**, 10, 194–202. [Google Scholar] [CrossRef] - Redfern, M.A.; Checksfield, M.J. A Study into a New Solution for the Problems Experienced with Pole Slipping Protection. IEEE Trans. Power Deliv.
**1998**, 13, 394–404. [Google Scholar] [CrossRef] - Kumar, N.; Nagaraja, D.R.; Khincha, H.P. A smart and adaptive scheme for generator out of step protection. In Proceedings of the 2015 IEEE Innovative Smart Grid Technologies-Asia (ISGT ASIA), Bangkok, Thailand, 3–6 November 2015. [Google Scholar]
- Alinezhad, B.; Karegar, H.K. Out-of-Step Protection Based on Equal Area Criterion. IEEE Trans. Power Syst.
**2017**, 32, 968–977. [Google Scholar] [CrossRef] - Paudyal, S.; Ramakrishna, G.; Sachdev, M.S. Application of Equal Area Criterion conditions in the Time Domain for Out-of-Step Protection. IEEE Trans. Power Deliv.
**2010**, 25, 600–609. [Google Scholar] [CrossRef] - Haner, J.M.; Laughlin, T.D.; Taylor, C.W. Experience with the RRdot Out of Step Relay. IEEE Trans. Power Syst.
**1986**, PWRD-1, 35–39. [Google Scholar] [CrossRef][Green Version] - Fan, D.; Centeno, V. Adaptive out-of-step protection schemes based on synchropahasors. In Proceedings of the IEEE Power & Energy Society General Meeting, National Harbor, MD, USA, 27–31 July 2014. [Google Scholar]
- Sauhats, A.; Utans, A.; Antonovs, D.; Svalovs, A. Angle Control-Based Multi-Terminal Out-of-Step Protection System. Energies
**2017**, 10, 308. [Google Scholar] [CrossRef][Green Version] - Orešković, G.; Bacinger, I.; Dvekar, Đ. Active Power Oscillation cause detection in HPP Dubrava applying generator power angle measurement. In Proceedings of the 7th HRO CIGRE Session, Cavtat, Croatia, 21–23 November 2005. [Google Scholar]
- Brezovec, M.; Brkljac, B.; Kuzle, I. Influence of operating conditions on hydrounit power oscillations. In Proceedings of the Eurocon 2013 Conference, Zagreb, Croatia, 1–4 July 2013; pp. 1453–1459. [Google Scholar]

**Figure 1.**Load angle curve [11].

**Figure 2.**Power transmission capability of the normal system (blue curve) and the system with fault (red curve) [11].

**Figure 3.**Graphical representation of the relation of rotor position, magnetic field and load angle.

**Figure 7.**Relation of terminal voltage signal and air gap signal as load angle changes. The red curve represents the generator terminal voltage signal, the blue curve represents the air gap sensor signal when the generator is in the no-load operation mode and the green curve represents the air gap sensor signal when the generator is loaded.

**Figure 13.**Results of the load angle measurement when the load angle correction function is not applied. The red dots represent the load angle values, and the blue curve the output of the keyphasor sensor.

**Figure 14.**Results of determining the correction data in relation to the keyphasor sensor signal obtained in the algorithm testing. The red dots represent the correction data values.

**Figure 15.**Results of the load angle measurement when the load angle correction function is applied. The red dots represent the corrected load angle values.

**Figure 16.**Testing results of the load angle measurement algorithm of the synchronous generator under steady-state conditions. The red curve represents the active power measurements, the green curve represents the reactive power measurements and the blue curve the load angle measurements.

**Figure 17.**Testing results of the load angle measurement algorithm of the synchronous generator under continuous change of the active power. The red curve represents the active power measurements and the blue curve the load angle measurements.

**Figure 18.**Testing results of the load angle measurement algorithm of the synchronous generator under a change in first the active and then the reactive power. The red curve represents the active power measurements, the green curve represents the reactive power measurements and the blue curve the load angle measurements.

**Figure 19.**Simulation results of active power of Generator 2 during the three-phase fault with the fault duration of 170 ms.

**Figure 20.**Simulation results of reactive power of Generator 2 during the three-phase fault with the fault duration of 170 ms.

**Figure 21.**Simulation results of the load angle of Generator 2 during the three-phase fault with the fault duration of 170 ms.

**Figure 22.**Simulation results of speed of Generator 2 during the three-phase fault with the fault duration of 170 ms.

**Figure 23.**Simulation results of active power of Generator 2 during the three-phase fault with the fault duration of 172 ms.

**Figure 24.**Simulation results of reactive power of Generator 2 during the three-phase fault with the fault duration of 172 ms.

**Figure 25.**Simulation results of the load angle of Generator 2 during the three-phase fault with the fault duration of 172 ms.

**Figure 26.**Simulation results of speed of Generator 2 during the three-phase fault with the fault duration of 172 ms.

**Table 1.**Technical specifications of the capacitive air gap sensor Veski CGS020210 used in the testing.

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

Probe type | CGP-02 | |

LM type | CGL0202 | |

Probe dimension | mm | 135 × 32 × 17 |

LM dimension | mm | 125 × 80 × 60 |

Measuring range | mm | 3 to 15 |

Power supply | VDC | 18 to 36 |

Voltage output | VDC | 2 to 10 |

Current output | mA | 4 to 20 |

Operating temperature | °C | −15 to 70 |

Full range accuracy | % | ±3 |

Parameter | Symbol | Unit | Generator 1 | Generator 2 |
---|---|---|---|---|

Nominal power | S_{n} | MVA | 42 | 42 |

Nominal active power | P_{n} | MW | 39.9 | 39.9 |

Nominal voltage | U_{Gn} | kV | 6.3 ± 7.5% | 6.3 ± 7.5% |

Power factor | cosφ_{n} | 0.95 | 0.95 | |

Nominal speed | n | rpm | 125 | 125 |

Nominal frequency | f_{n} | Hz | 50 | 50 |

Inertia constant | T_{A} | s | 1.05 | 1.05 |

Moment of inertia | J(I) | t m^{2} | 1150 | 1150 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Višić, I.; Strnad, I.; Marušić, A. Synchronous Generator Out of Step Detection Using Real Time Load Angle Data. *Energies* **2020**, *13*, 3336.
https://doi.org/10.3390/en13133336

**AMA Style**

Višić I, Strnad I, Marušić A. Synchronous Generator Out of Step Detection Using Real Time Load Angle Data. *Energies*. 2020; 13(13):3336.
https://doi.org/10.3390/en13133336

**Chicago/Turabian Style**

Višić, Ivan, Ivan Strnad, and Ante Marušić. 2020. "Synchronous Generator Out of Step Detection Using Real Time Load Angle Data" *Energies* 13, no. 13: 3336.
https://doi.org/10.3390/en13133336