1Dynamics and Control of Electric Power Systems

Systemdynamik und Leittechnikin der elektrischen Energieversorgung

High Lights 2011

2Figure 1.1. Schematic diagram of different time scales of power system controls.

3Figure 1.2. The structure of the hierarchical control systems of a power system.

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6Forecast of wind power production, western Denmark

7Figure 1.5. Duration curve showing the use of different kinds of power plants.

8Figure 2.1. The frequency in different locations in an electric power system after a disturbance.

9Figure 2.2.Simplified representation of a power system consisting of a single generator connected to the same bus as the load.

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Figure 2.4. Linearized model of the power system frequency dynamics.

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Figure 2.6. Model of power system without control.

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Figure 2.7. Frequency responses of uncontrolledpower system (theoretical) to step in Pload. (DL = 1/200 Hz/MW)

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Figure 2.8. Basic control structures of electric power systems.

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Figure 2.9. Temporal structure of control reserve usage after a disturbance.

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Figure 3.1. Schematic drawing of the primary control installed ina thermal unit. HP = High Pressure Turbine. LP = Low Pressure turbine.

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Figure 3.3. Static characteristic of primary control.

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Figure 3.8. Two generator system.

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Figure 3.9. Speed droop characteristics for a two-machine system.

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Figure 3.11. Dynamic frequency model of the power system with primary-controlled power plants.

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Figure 3.13. Simplified representation of a power system with two areas.

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Figure 3.14. Two-area dynamic model including tie-line flows.

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Figure 3.16. Step response for the system in Figure 3.15 with primary control only, i.e. no AGC.

(Area 2 much bigger than Area 1)

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Figure 3.17. Steam turbine configurations and approximate linear models. Nonreheat and tandem compound, single reheat configurations.

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Figure 3.22. Schematic drawing of hydro turbine with water paths.

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Assumptions:

Bernoullis equation:

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The system can be written in standard form:

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Transfer function:

with as

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Figure 3.24. The variation of the produced power, Dy , after a step change in the control valve.

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Figure 3.26. Model of turbine governor for hydro turbine.

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Figure 3.27. Frequency variation after a step in DPload .

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Figure 4.1.Two area system with AGC.

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Figure 4.2.Controller for AGC.

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Non-Interactive Control (AGC)

1/i iB S

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Figure 4.6. Dynamic model of two-area system with AGC.

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Figure 4.5. Dynamic response of two-area system with AGC.Area 2 much bigger than Area 1. Disturbance in Area 1.

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Figure 5.1. Definition of quantities in Parks transformation.

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Figure 5.2. Schematic picture of the transformed system.

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Figure 5.4. Graphical description of the voltage equationsand the coupling between the equivalent circuits.

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The above expression can now be used to express thechange of the flux in the d-winding:

where the subtransient inductance (in the d-axis)has been defined as

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This current decays much slower than the current in D-winding.Can be regarded as constant!

Thus the time constant for the decay of the D-winding current is

The subtranisent open circuit time constant in the d-axis

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Table 5.1. Typical synchronous machine parameters.

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Fourth order model

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Third order model

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Voltage Control in Power Systems

Reactive Power

Voltage

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Factors Influencing the Voltages

Terminal voltages of synchronous machines

Reactive shunt elements

Turns ratio of transformers

Control of FACTS devices

Impedances of lines

Loading of transmission lines

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Figure 6.1. Schematic picture of synchronous machine andassociated control systems.

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Exciter Systems

1. DC Excitation Systems

2. AC Excitation Systems

3. Static Excitation Systems

1. & 2. Rotating, 3. Static

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Static Load Models

ZIP Model:

0

1

2

012

0; 0,1,2,ik i

=

=

=

=

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Figure 7.5. Transient behaviour of dynamic load.

Slide Number 1 Slide Number 4Slide Number 5Forecast of wind power production, western Denmark Non-Interactive Control (AGC) Slide Number 37Slide Number 38Slide Number 39 Slide Number 42Slide Number 43 Slide Number 45Slide Number 46Voltage Control in Power Systems Factors Influencing the Voltages Exciter SystemsStatic Load Models