# Mathematical model for the doubly fed wound-rotor generator

## Abstract

Present electrical power generators dictate that the prime movers operate at constant speed. This is necessary because the power must be generated at constant frequency. However, some prime movers are, by their nature, not constant-speed-devices, such as hydroturbines and wind turbines. Various schemes have been proposed that remove the constant-speed requirement. The scheme investigated in this paper is a wound-rotor generator, whose rotor is excited with variable-frequency power. This paper develops a mathematical model which predicts what the rotor excitation must be, if the stator is to operate at constant frequency and voltage. A machine with three-phase rotor and stator is analyzed. It is described by two sets of circuit equations; one set for the stator, another for the rotor. Under balanced conditions, these two sets reduce to only two equations. In practical application, these machines are operated with constant stator-terminal voltage. When this constraint is applied to the two circuit equations, expressions for currents and voltages, on both rotor and stator are obtained. These same circuit equations can be used to generate a set of volt-ampere equations. If the expressions for current and voltages are substituted into the volt-ampere equations, a relationship between active stator volt-amperes, active rotor volt-amperes,more »

- Authors:

- Publication Date:

- Research Org.:
- National Aeronautics and Space Administration, Cleveland, OH (USA). Lewis Research Center

- OSTI Identifier:
- 5717102

- Report Number(s):
- DOE/NASA/20320-48; NASA-TM-83454; CONF-830705-5

ON: DE83018232

- DOE Contract Number:
- AI01-76ET20320

- Resource Type:
- Conference

- Resource Relation:
- Conference: IEEE Power Engineering Society summer meeting, Los Angeles, CA, USA, 17 Jul 1983

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 17 WIND ENERGY; ELECTRIC GENERATORS; MATHEMATICAL MODELS; ANALYTICAL SOLUTION; DIFFERENTIAL EQUATIONS; ELECTRIC POWER; EXCITATION; ROTORS; ENERGY-LEVEL TRANSITIONS; EQUATIONS; POWER; 170603* - Wind Energy Engineering- Power-Conversion Systems

### Citation Formats

```
Brady, F J.
```*Mathematical model for the doubly fed wound-rotor generator*. United States: N. p., 1983.
Web.

```
Brady, F J.
```*Mathematical model for the doubly fed wound-rotor generator*. United States.

```
Brady, F J. Sat .
"Mathematical model for the doubly fed wound-rotor generator". United States.
```

```
@article{osti_5717102,
```

title = {Mathematical model for the doubly fed wound-rotor generator},

author = {Brady, F J},

abstractNote = {Present electrical power generators dictate that the prime movers operate at constant speed. This is necessary because the power must be generated at constant frequency. However, some prime movers are, by their nature, not constant-speed-devices, such as hydroturbines and wind turbines. Various schemes have been proposed that remove the constant-speed requirement. The scheme investigated in this paper is a wound-rotor generator, whose rotor is excited with variable-frequency power. This paper develops a mathematical model which predicts what the rotor excitation must be, if the stator is to operate at constant frequency and voltage. A machine with three-phase rotor and stator is analyzed. It is described by two sets of circuit equations; one set for the stator, another for the rotor. Under balanced conditions, these two sets reduce to only two equations. In practical application, these machines are operated with constant stator-terminal voltage. When this constraint is applied to the two circuit equations, expressions for currents and voltages, on both rotor and stator are obtained. These same circuit equations can be used to generate a set of volt-ampere equations. If the expressions for current and voltages are substituted into the volt-ampere equations, a relationship between active stator volt-amperes, active rotor volt-amperes, and shaft power is obtained. This relationship permits a new interpretation of the power flow.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1983},

month = {1}

}