## Dynamic generator model

The operation of a (synchronous) generator is based on the Maxwell's second equations or equivalently, Faraday's law of electromagnetic induction. This law states that when the field is excited and rotated, voltages will be induced in the three stator phases.

Rotor

Rotor

Figure 3.24: Schematic representation of an elementary three-phase, two-pole synchronous generator.

phasec phasec

The fields produced by the stator winding currents are assumed to be sinusoidally distributed around the airgap. This assumption ignores the space harmonics and as a result, the induced stator voltages (or electromagnetic force EMF) will vary sinusoidally with time. In steady-state, the three sine waves will be displaced 120° electrical degrees in time as a result of the phases being displaced 120° in space. Using generator sign convention, the stator currents are defined positive flowing out of the machines terminals and the expressions for the induced stator voltages become

with Ra, Rb, and Rc the resistance of stator a-phase, 5-phase and c-phase, ia, ib and ic the stator currents, and 'a, 'b and 'c the stator flux linkages respectively. The stator resistances are constant when skin effect and effects of temperature are neglected [219].

The equation for the field winding voltage is uf = —Rf • if d'f ~dT

with Rf, if and if the field winding resistance, current, and flux linkage respectively. The equations for the short-circuited (i.e. u1d = 0) direct-axis damper winding and short-circuited (i.e. u1q = 0) quadrature-axis damper winding are

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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