Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis
Abstract
:1. Introduction
2. Modeling Methods for Transients Calculation
2.1. Modeling of a Sudden Three-Phase Short-Circuit Using the FEM
- all of the coils in windings have equal numbers of conductors and therefore equal resistance; windings are placed symmetrically on poles, enabling the analysis of one repeating segment of the generator;
- the ratio of the core length and the end winding length of the generator is 3.2, and allows the 2D model to be applicable;
- the influence of the skin effect, which can appear in excitation or in armature winding conductors, is neglected;
- the stray current and the eddy current are excluded because the electric conductivity of iron can also be neglected;
- embedded materials are isotropic, the hysteresis loop is neglected, and the iron permeability depends on the magnetic field strength;
- the rotor speed variations throughout the transients, due to high inertia of mass, are also neglected; and
- the sources used to feed the windings are assumed to be perfect.
- is the electric field strength in the conductors,
- is the lux density,
- is the magnetic field strength,
- is thecurrent density,
- C is the curve bounding the surface S,
- S is the plane in which the field is calculated, and
- is the unit vector normal to surface S.
2.2. Sudden Short-Circuit by a Dynamic Model
- [U] is the matrix of voltage,
- [i] is the matrix of current,
- [R] is thematrix of resistance,
- [L] is the matrix of inductance,
- ωel is the electric angle velocity of rotor, and
- γ is the electric angle between the axis of stator phase “a” and the d-axis of rotor.
- Ψd is the magnetic flux in armature winding in d-axis,
- Ψf is the magnetic flux in excitation winding,
- ΨD is the magnetic flux in damping winding in d-axis,
- Ψq is the magnetic flux in armature winding in q-axis,
- ΨQ is the magnetic flux in damping winding in q-axis,
- ud is the transformed armature winding in d-axis,
- uf is the excitation voltage,
- uq is thetransformed armature winding in q-axis,
- kd is the linkage factor of armature winding in d-axis,
- kf is the linkage factor of excitation winding,
- kD is the linkage factor of damping winding in d-axis,
- kq is the linkage factor of armature winding in q-axis,
- kQ is the linkage factor of damping winding in q-axis,
- is the transient inductance of damping and excitation windings,
- is the transient inductance of armature and damping windings,
- is the transient inductance of excitation and damping windings,
- is the transient inductance of armature and excitation windings,
- is the transient inductance of excitation and armature windings,
- is the transient inductance of damping and armature windings,
- is the subtransient inductance of armature winding in d-axis,
- is the subtransient inductance of excitation winding,
- is the subtransient inductance of damping winding in d-axis,
- is the subtransient inductance of armature winding in q-axis,
- is the subtransient inductance of damping winding in q-axis,
- is the subtransient time constant of the armature winding at short-circuit in d-axis,
- is the subtransient time constant of the armature winding at short-circuit in q-axis,
- is the subtransient time constant of the damping winding at short-circuit in d-axis,
- is the subtransient time constant of the damping winding at short-circuit in q-axis,
- is the subtransient time constant of the excitation winding at short-circuit, and
- H is the inertia constant.
3. Transient Analysis Using a Dynamic Simulation Model
- d-axis synchronous reactance Xd = 1.06 p. u.,
- d-axis transient reactance Xd′ = 0.28 p. u.,
- d-axis subtransient reactance Xd″ = 0.192 p. u.,
- q-axis synchronous reactance Xq = 0.61 p. u.,
- q-axis subtransient reactance Xq″ = 0.176 p. u.,
- leakage reactance Xl = 0.14 p. u.,
- d-axis transient short-circuit time constant Td′ = 1.56 s,
- d-axis subtransient short-circuit time constant Td″ = 0.05 s,
- q-axis subtransient open-circuit Tqo″ = 0.09 s,
- inertia constant H = 3.2 s,
- friction factor F = 0, and
- stator resistance Rs = 0.0161 p. u.
4. Results and Discussion
4.1. The Results of the FEM Calculation Method
4.2. The Results of Three-Phase Fault on the Generator in the Dynamic Simulation Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Tomičić, B.; Šumiga, A.; Nađ, J.; Srpak, D. Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis. Appl. Sci. 2021, 11, 11734. https://doi.org/10.3390/app112411734
Tomičić B, Šumiga A, Nađ J, Srpak D. Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis. Applied Sciences. 2021; 11(24):11734. https://doi.org/10.3390/app112411734
Chicago/Turabian StyleTomičić, Branko, Antonija Šumiga, Josip Nađ, and Dunja Srpak. 2021. "Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis" Applied Sciences 11, no. 24: 11734. https://doi.org/10.3390/app112411734
APA StyleTomičić, B., Šumiga, A., Nađ, J., & Srpak, D. (2021). Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis. Applied Sciences, 11(24), 11734. https://doi.org/10.3390/app112411734