1. Placing Controllers in a System

2. Overview of Class So Far… l General Introduction l Deregulation l Traditional approaches to control l Static devices

3. Type of problems l Steady State l Transient Stability l Inter-Area Oscillations l Subsynchronous Resonance l Voltage Stability

4. Introduction to FACTS l Detailed analysis of devices yThyristor controlled inductor ySVC yStatcom yTCSC

5. System Modeling l Simplified models for use in system simulations and analysis yStatcom yTCSC (see Reference [1]) yUPFC

6. Set up system equations to include FACTS devices l Get block diagrams or differential equations for device l Define device states l Define device inputs l Express device model in terms of existing system states & device states l Augment system equations

7. Use these devices to fix system problems!

8. OK, Say you work at an ISO & are in charge of ensuring system reliability. You've had 5 major blackouts in the last 3 years that have involved the propagation of problems from one part of the system to another. The utility members are convinced that the addition of a FACTS device or two will solve the problems & they even agree to pay!

9. Now what do you do?... l Brainstorming Activity: yWhat things do you need to worry about? yBreak into groups of 2 or 3 yTake 3 minutes & write down as many things as you can yNo criticism allowed, Go for variety, Go for quantity not quality

10. Questions: l Where do I put it? Controller Location l What should it do?Controller Function

11. Things to consider: l More than one problem l More than one system condition l More than one mode l More than one tool

12. Problems l Steady State yInsure operating point is within acceptable limits l Interarea Oscillations yDamp eigenvalues

13. l Transient Stability yProvide sufficient synchronizing and damping torque l Subsynchronous Resonance yAvoid resonance frequencies l Voltage Stability yStabilize eigenvalues and avoid bifurcations

14. Interarea Oscillation Mitigation l Analysis Tools (Mostly Linear) yControllability and Observability yParticipations ySensitivities yPower Oscillation Flows

15. Linearized System x’ = Ax + Bu y = Cx + Du Eigenvalues are i, i = 1, nstates l Right Eigenvectors r i, R is matrix of r i 's Left Eigenvectors (rows) i, L is matrix of i 's l L = R - 1

16. Perform variable transformation to Jordan Form l x = Rz(Inverse transform z = Lx) l Substituting into system equations... Rz’ = AR z + B u y = CR z + Du

17. Multiply through by L = R -1 LRz’ = z’ = LAR z + LB u y = CR z + Du

18. Controllability and Observability l Modal controllability matrix = LB ytells how strongly connected the inputs (u's) are to each of the modes l Modal observability matrix = CR ytells how well we can measure or "see" each mode in the outputs (y's)

19. Participations l Connection strengths between modes and states l General participation yp i hk = r i h l hk ylink between i th (obs.) & k th (con.) states through mode h l Participation Factors yp i h = r i h l h i ylink between mode h & state i

20. Eigenvalue Sensitivities i ’ =  i /  p l p some parameter of the system l Tells how easily we can move an eigenvalue by changing a parameter In general, i ' = l i A' r i

21. Sensitivities are also related to participations p ihk = h ’ for p = a ki (element of A) p ih = h ’ for p = a kk (diagonal element) u(t) x(t) p rest of system xixi xkxk

22. Sensitivity with Controllers l The "Hybrid System"

23. The Power System x’ = Ax + Bu y = Cx l assume no direct connection between y & y 2 l The controller transfer function F(s,p) is the only place p shows up

24. Sensitivity for Hybrid System i ’ =  i /  p = l i B {  /  p [F(s,p)]| s= i } C r i l related to the controllability and observability measures and to the controller transfer function (see Reference [5])

25. Uses of Sensitivities l Location of controllers Magnitude of ’ tells the displacement of the eigenvalue if gain is equal to 1 l Large magnitude indicates controller is a good candidate for improving a mode Phase ’ of gives the direction of the eigenvalue's displacement in the imaginary plane

26. Introduce devices likely to influence these characteristics l Simulations and Trial & Error

27. Tuning of a controller... Adjust the phase compensation of the controller so that ’ has a phase of 180 degrees with controller in place l Adjust the gain of the controller to achieve the desired amount of damping

28. Power Oscillation Flows l Map where oscillations caused by a single eigenvalue appear in the system n x(t)   c k e k t r k k = 1 l c k is the initial condition in Jordan Space

29. l The idea is to choose c k 's so that only one mode is perturbed, i.e. c i = 1 and c k = 0 for all k not equal i then x(t) = r i e i t l this solution can then be propagated through the system equations to find the power flow on key lines (or some other variable for that matter)

30. Placing a FACTS device using participations, sensitivities, etc. l Simple & Fast l Detailed & More Accurate

31. Transient Stability and FACTS l Usually concerned with providing adequate damping and synchronizing torque l Often design using linear techniques and test with the nonlinear system

32. Nonlinear Methods l Normal forms of vector fields for extending the linear concepts to the nonlinear regions. l Second-order oscillations, participations, controllability & observability

33. Energy Methods l Lyapunov-based methods for determining stability indices l Tracking of energy exchanges during a disturbance

34. Control Strategy l Determine weak points in system yPoorly damped oscillations yLack of synchronizing torque yLarge power swings yLarge energy exchanges yShort critical clearing times yMulti-machine instabilities

35. References [1]Paserba, J. J., N. W. Miller, E. V. Larsen, and R. J. Piwko "A Thyristor Controlled Series Compensation Model for Power System Stability Analysis" IEEE Trans. on Power Delivery, Vol. 10?, (July 1994): 1471-1478. [2]Chan, S. M. "Modal Controllability and Observability of Power- System Models" International Journal of Electric Power and Energy Systems, Vol. 6, No. 2, (April 1994): 83-89. [3]Rouco, L., and F. L. Pagola "An Eigenvalue Sensitivity Approach to Location and Controller Design of Controllable Series Capacitors for Damping Power System Oscillations" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-547- PWRS-0-01-1997.

36. [4]Ooi, B. T., M. Kazerani, R. Marceau, Z. Wolanski, F. D. Galiana, D. McGillis, and G. Joos "Mid-Point SIting of FACTS Devices in Transimssion Lines" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-292-PWRD-0-01-1997. [5]Pagola, F. L., I. J. Perez-Arriaga, and G.C. Verghese "On Sensitivities, Residues, and Participations: Application to Oscillatory Stability Analysis and Control" IEEE Trans. on Power Systems, Vol. 4, No. 2, (February 1989): 278-285. [6]Messina, A. R., J. M. Ramirez, and J. M. Canedo C. "An Investigation on the use of Power Systme Stabilizers for Damping Inter-Area Oscillations in Longitudinal Power Systems" IEEE-PES 1997 Winter Power Meeting, Paper No. PE-492-PWRS-0-01-1997. [7]Zhou, E. Z. "Power Oscillation Flow Study of Electric Power Systems" International Journal of Electric Power and Energy Systems, Vol. 17, No. 2, (1995): 143-150.