1. Challenges in Modelling Active Electric Power Networks Dr. S. K. Chakravarthy Department of Elect. Engg., KFUPM

2. Aspects to be addressed b b The conventional electric power transmission network. b b Analytical methods used. b b What is an active electric power transmission network? b b Use of numerical simulations. b b Why is a new analytical method required? b b Some advantages of the new approach.

3. Aspect One b b The conventional electric power transmission network.

4. RL C1 Modelling a Conventional Power Transmission Network

5. Purpose of conventional transmission networks b b An electric power transmission network is designed to transfer bulk power between two points. b b Performance of an electric power transmission network is obtained from the nominal Pi-equivalent circuit.

6. Aspect Two b Analytical methods used.

7. Analytical Methods Used

8. b b For initial values of control vector u and load vector p one can find the state variable x. b b State variable x represents the bus voltages in the network.

9. Analytical Methods Used b b Knowing the initial values of ( x, u,p) one obtains the solution at a future instant t. b b This solution represents the slowly evolving dynamics of the system (due to the moment of inertia of rotating machines.

10. Aspect Three b What is an active electric power transmission network?

11. RL C1C2 L-TCR Two anti-parallel thyristor-pair for each phase. Bus-1 V1 Bus-2 V2 An Active Power Transmission Network

12. An active electric power network? b b The extent of power that can be transferred between two points can be controlled by FACTS or Static VAR Systems. b b By the use of these local controllers, the surge impedance and propagation constant change rapidly.

13. An active electric power network? b b The changes in these parameters can be enforced at least once every cycle. b b Consequently, the network parameters become time dependent (that is, they need to be represented by differential equations).

14. The Problem b b In modeling: The resonant frequencies of the network will (dynamically) change. The switching operation of the controllers makes the transmission network nonlinear. There is a distinct possibility of the occurrence of switching bifurcations.

15. Aspect Four b b Use of numerical simulations.

16. Analytical Solution (system involving fast and slow dynamics)

18. Aspect 5 b Why is a new analytical method required?

19. Why a new method? b b The odes along with the nonlinear transformation can solved by packages such as EMTP or EMTDC. b b However, one cannot rule out the possibility of numerical instability providing erroneous results. b b Numerical instability arises from the existence of zero eigenvalues in a nonlinear system.

20. Why a new method? b b The system of ode’s have zero eigenvalues. b b The inclusion of nonlinear transformations and the presence of zero eigenvalues will give rise to bifurcation leading to several periodic and aperiodic (numerical) oscillations.

21. Why a new method? b b Problem: The numerical solution of a stable (physical) system may be unstable. The conditions that may initiate any of these numerical instability depend on the initial conditions, which are never completely known.

22. Aspect Six b Some advantages of the new approach.

23. Advantages of the new approach. b b Provide tractability to a nonlinear system with large dimension such as a power system. b b The large dimensional nonlinear system can be modeled as an equivalent reduced order system.

24. Conclusions b In summary, the challenges involved in modelling active EPTN’s involve: Determining the number of eigenvalues with zero real parts for a large scale system;Determining the number of eigenvalues with zero real parts for a large scale system;  Eliminating the fast transient by determining the invariant manifold while still retaining their influence on the nonlinear behaviour of the system;  Eliminating time dependence by the method of averaging.

25. Conclusions Since the solutions are dependent on the choice of initial conditions, numerical methods must be integrated with symbolic processing software;Since the solutions are dependent on the choice of initial conditions, numerical methods must be integrated with symbolic processing software; Methods are required for dimensionally reducing the problem.Methods are required for dimensionally reducing the problem.

26. Conclusions THANK YOU FOR YOUR ATTENTION