Real-Time Simulation of Power Conversion in Doubly Fed Induction Machine
Abstract
:1. Introduction
2. Real-Time Simulators
3. Mathematical Model of the Electrical System with DFIM
3.1. Basics of Mathematical Modeling of Electrical Systems
3.1.1. Multipole Modeling of Electrical Systems—Basic Concept
- (1)
- The modeled electrical system is decomposed into individual structural elements, creating a substitute diagram in the form shown, e.g., in Figure 2, separating specific electric multipoles.
- (2)
- Nodes are identified for the entire system by determining the vector of nodes in the form (1) and the vector of integrals from node potentials of the modeled system in the form (8).
- (3)
- For each multipole (structural element), the appropriate PEk incidence matrices, matrices of node potentials, in Equation (2), integrals of node potentials, in Equation (4) and currents of external branches, in Equation (2) are determined.
- (4)
- The initial conditions of the modeled system are assumed.
- (5)
- For each multipole (structural element), respectively, the AEk and BEk, matrices appearing in Equation (3) are determined (the examples of determining these matrices for selected multipoles are described later in the article).
- (6)
- The AS and BS matrices are determined by formulas in (11).
- (7)
- The system of Equations (10) is numerically solved, obtaining values of the vector (8) of integrals from node potentials of the modeled system.
- (8)
- From the formula (7) values of the vector (4) of integrals from node potentials of individual multipoles are determined.
- (9)
- From Equation (3), the values of the vector (2) of currents in external branches for individual multipoles are determined.
- (10)
- If the conditions for continuing the simulation are fulfilled, there is a transition to point 5 of this algorithm; otherwise, the simulation will be stopped.
3.1.2. Method with Average Voltage Values at the Calculation Step—Basic Concept
3.2. Mathematical Models of Selected Structural Elements
3.2.1. Mathematical Model of a Replacement Three-Phase Voltage Source (E1)
3.2.2. Mathematical Model of a Ring Rotor Induction Machine (E2)
- The machine has a symmetrical stator and rotor design, and both the stator windings and the rotor are distributed in a way that provides a sinusoidal spatial distribution of the magnetic flow.
- The magnetic field in the machine consists of three components: stator winding leakage fields (magnetic field lines are associated only with stator windings), rotor winding leakage fields (magnetic field lines are associated only with rotor windings) and main field (magnetic field lines are simultaneously associated with stator windings and rotor).
- Saturation of the magnetic circuit is omitted, and linearity of the magnetization characteristics is assumed.
- There are no power losses in the magnetic core of the machine, and the phenomenon of magnetic hysteresis and eddy currents are omitted.
- The stator and rotor cores are groove-free, and slants for grooves are not included.
4. Examination of the Adequacy of the Proposed Mathematical Model
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Nominal Data | Parameters of Equivalent Circuits | ||||
---|---|---|---|---|---|
Rated power | 600 W | Stator current | 3.5 A/2.0 A | Stator resistance | 8.03 Ω |
Voltage | 220 V/380 V | Rotor current | 15 A | Rotor resistance (1) | 13.82 Ω |
Frequency | 50 Hz | Rated Torque | 6.3 N·m | Mutual inductance | 413.5 mH |
Rated speed | 920 rpm | Inertia Moment | 0.04 kg·m2 | Stator inductance | 38.6 mH |
Power factor | 0.64L | Rotor inductance (1) | 38.6 mH |
Nominal Data | Parameters of Equivalent Circuits | ||||
---|---|---|---|---|---|
Rated power | 1.8 MW | Stator current | 1772.1 A | Stator resistance | 4.554 mΩ |
Voltage | 0.69 kV | Rotor current | 578.9 A | Rotor resistance (1) | 5.749 mΩ |
Frequency | 50 Hz | Rated Torque | 11.73 kN·m | Mutual inductance | 2.42 mH |
Conversion ratio | 3.061 | Max Torque | 31.7 kN·m | Stator inductance | 0.178 mH |
Power factor | 0.88L | Inertia Moment | 68.92 kg·m2 | Rotor inductance (1) | 0.217 mH |
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Kłosowski, Z.; Cieślik, S. Real-Time Simulation of Power Conversion in Doubly Fed Induction Machine. Energies 2020, 13, 673. https://doi.org/10.3390/en13030673
Kłosowski Z, Cieślik S. Real-Time Simulation of Power Conversion in Doubly Fed Induction Machine. Energies. 2020; 13(3):673. https://doi.org/10.3390/en13030673
Chicago/Turabian StyleKłosowski, Zbigniew, and Sławomir Cieślik. 2020. "Real-Time Simulation of Power Conversion in Doubly Fed Induction Machine" Energies 13, no. 3: 673. https://doi.org/10.3390/en13030673