Energy Conversion and Transport George G. Karady & Keith Holbert EEE 360 Energy Conversion and Transport George G. Karady & Keith Holbert Chapter 6 Synchronous Machine 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Lecture 15 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines The DC excitation current in the rotor generates a flux. The turbine drives the rotor and produces a rotating flux The rotation cause flux changes in the windings The rotating flux induce a ac three phase voltage in the stator winding. This is the rotor induced voltage in the stator. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines The generator is loaded The load current produces a rotating flux This rotating flux induces a ac three phase voltage in the stator winding. This voltage is subtracted from the induced voltage. represented by a voltage drop on the synchronous reactance The equivalent circuit of a synchronous generator is a voltage source and a reactance connected in series 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.3 Generator Application Power angle: Angle between the dc excitation current generated induced voltage and the terminal voltage 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.3 Generator Application 6.3.1 Loading: power is less than angle 90 deg All generators in the system are connected in parallel All generators rotates with the synchronous speed The load can be increased by increasing the input mechanical power by regulating the turbine impute power The speed does not change, the power angle increases Maximum power angle is 90 degree, beyond that operation is unstable 6.3.2 Reactive power regulation When the excitation is: Increased, the generator reactive power also increases; Decreased, the generator reactive power also decreases 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.3.3 Synchronization Verify that the phase sequences of the two systems are the same. Adjust the machine speed with the turbine that drives the generator until the generator voltage frequency is nearly the same as the frequency of the network voltage. Adjust the terminal voltage of the generator by changing the dc field (rotor) current until the generator terminal voltage is almost equal to the network voltage. Acceptable limit is 5%. Adjust the phase angle of the generator terminal voltage by regulating the input power until it is nearly equal with the phase angle of the network voltage. Acceptable limits are about 15°. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.3.4 Static stability Generator Transmission line Network 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.19 One-line diagram of a simple power system Figure 6.20 Single-phase equivalent circuit of the network in Figure 6.19 . 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine System Data 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine 1/18/2019 360 Chapter 6 Synchronous Machine

The generator and network power vs power angle Stable operation Unstable operation Maximum power Operation point 1/18/2019 360 Chapter 6 Synchronous Machine

Maximum power transmitted 1/18/2019 360 Chapter 6 Synchronous Machine

6.4 Induced Voltage Synchronous Reactance Calculation 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4 Induced Voltage and Synchronous Reactance Calculation 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.26 Rotor-generated magnetic field in the simplified generator. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4.1 Induced Voltage Ampere’s circuital law for this magnetic loop yields If iron core is neglected 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4.1 Induced Voltage Figure 6.27 Rotor generated flux density distribution along the rotor surface Square wave flux equation 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4.1 Induced Voltage The base component is calculated using the Fourier series 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4.1 Induced Voltage Substitution of current and flux density results in: Flux integral 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines 6.4.1 Induced Voltage Substitution of current and flux density results in: Flux integral 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Rotating Flux Generation 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.29 Arrangement for calculation of load current generated flux. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.30 Phase A load current generated ac flux. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.31 AC flux generated by the phase currents. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.32 Rotating flux generated by the phase currents 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.33 Flux linkages with phase A. 1/18/2019 360 Chapter 6 Synchronous Machine

Exercises using MATCAD 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.34 One-line diagram of synchronous generator network Figure 6.35 Single-phase equivalent circuit of synchronous generator network. Figure 6.36 Simplified single-phase equivalent circuit of synchronous generator network. 1/18/2019 360 Chapter 6 Synchronous Machine

360 Chapter 6 Synchronous Machine Synchronous Machines Figure 6.37 Power delivered to the network as a function of power angle. 1/18/2019 360 Chapter 6 Synchronous Machine