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Post-Contingency Equilibrium Analysis

Post-Contingency Equilibrium Analysis. Rodney Yeu May 13, 2005. Reliability. Adequacy

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Post-Contingency Equilibrium Analysis

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  1. Post-Contingency Equilibrium Analysis Rodney Yeu May 13, 2005

  2. Reliability • Adequacy • The ability of the electric system to supply the aggregate electrical demand and energy requirements of their customers at all times, taking into account scheduled and reasonably expected unscheduled outages of system elements. • Security • The ability of the electric systems to withstand sudden disturbances such as electric short circuits or unanticipated loss of system elements.

  3. Contingency Analysis • Assess power system security • Study outage events due to overloads • Alarm operators to potential overloads • Calculation of the power flow with variation in the network topology • Single line outages will be simulated

  4. Post-Contingency Equilibrium Analysis • Post Contingency • State of power system after a contingency has occurred • Post-Contingency Equilibrium Analysis • Post contingency state of a power system that take into account the states of the generators and the control inputs • Solution of the equilibrium machine equations along with the network constraints

  5. Generator • Flux-Decay Model • Three phase synchronous machine model • Dynamics related to field winding and the rotor

  6. Exciter • IEEE Type-I • Dynamics of field voltage produced by the exciter, the rate feedback of the voltage regulator, and the input of the exciter

  7. Turbine Governor • Steam Turbine Governor • Dynamics of power into the synchronous machine and power from the steam valve position

  8. Network Constraints • Algebraic constraints • Expression of the generator terminal KVL and net power flow of network

  9. Generator References • Calculation • Start from solved base case power flow • Solve the equilibrium model for the references • Post-Contingency State • References does not change from base case • Determines the power and voltage of the generator

  10. Post-Contingency Equilibrium Setup • Angle Reference • New Dynamic States

  11. Post-Contingency Equilibrium Setup • Set the time derivatives to zero and eliminate states that are easily found by substitution

  12. Post-Contingency Equilibrium Setup • Algebraic generator terminal and network constraints

  13. Variable Comparison • Contingency Analysis • Independent • Dependent • Post-Contingency Equilibrium Analysis • Independent • Dependent

  14. Full Newton Method • Taylor Series • Iteration • Involves calculation of 5m+2n× 5m+2n Jacobian matrix

  15. Utilization of Power Flow Program • Part of the network constraint equations are already solved by the power flow program • Alternative schemes to solve for equilibrium states • Power flow program solves these network constraint equations • Secondary program solves the rest of the equilibrium equations

  16. Compute Base Case Power Flow Calculate Reference Values and Initial Guess Take Out Transmission Line k=1 Update P and V and Calculate Power Flow Calculate V(k+1) and P(k+1)by solving Machine Equations k = k+1 No Yes Done Utilization of Power Flow Program

  17. Power Flow • Power flow • Variables • Dependent: • Independent: • Equations

  18. Partitioned Newton Method • Machine • Variables • Dependent • Independent

  19. Partitioned Newton Method • Machine • Equations

  20. Decoupled Newton Method • Calculate machine speed using only the slack bus machine equations • Calculation of voltage magnitude and real power output for each machine independent from other machine states • Easy way to incorporate different machine models to program

  21. Decoupled Newton Method • Power flow • Dependent: • Independent: • Slack bus • Dependent: • Independent: • Generator i • Dependent: • Independent:

  22. Decoupled Newton Method • Slack bus machine calculation need to be made first • Determine the machine speed of the system • Slack bus angle updated for use in other machine calculation • PV bus machine calculation can be made in arbitrary order

  23. Simulation • Matlab 7.0.1 • Full Newton Method • Partial Newton Method • Decoupled Newton Method • Power System Toolbox 2.0 • Power flow • PSS/E 30 • Dynamic simulation

  24. WECC Case • 9 Buses • 3 Generators • 9 Transmission Lines • Total System Load • Real: 315 MW • Reactive: 115 MVars • 3 Stable single line outages

  25. WECC Maximum Voltage Magnitude Difference

  26. WECC Maximum Real Power Difference

  27. 57-Bus Case • 57 Buses • 6 Generators • 80 Transmission Lines • Total System Load • Real: 1250.8 MW • Reactive: 336.4 MVars • 78 Stable single line outages

  28. 57-Bus Maximum Voltage Magnitude Difference

  29. 57-Bus Maximum Real Power Difference

  30. Conclusion • The real power output and the terminal voltage magnitude of a generator changes in the post-contingency equilibrium state • A power flow program can be utilized to calculate the post-contingency equilibrium state • Each generator calculation can be decoupled when utilizing the power flow program to calculate the post-contingency equilibrium state

  31. Future Works • Optimal multiplier for the Newton’s Method • Other methods to calculate the post-contingency equilibrium state using a power flow program • Simulation with other generator, exciter, turbine and governor models • Simulation on different power systems

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