A Practical Comprehensive Approach to PMU Placement for Full Observability

1. A Practical Comprehensive Approach to PMU Placement for Full Observability James Ross Altman Presented to Virgilio Centeno Jaime de la Ree Yilu Liu January 28, 2008 Blacksburg, VA

2. Developing a PMU Placement Strategy • Should be Practical • Full observability • Work well for real systems and adaptable to your individual system • Should be Comprehensive • Cover 3 main topics: model development, placement algorithm, installation strategy

3. Northeast India • 346 Buses (after reduction) • 575 Branches • 60 zero injection buses • 1 existing PMU in system

4. Observability • “Power System Observabilityrefers to the fact that measurement sets and their distribution are sufficient for solving the current state of power systems.” • Minimal PMU placement set - a set of buses that require PMU deployment to meet the minimum requirements of full observability.

5. Rule #1-All buses neighboring a bus with a PMU are observable themselves

6. Rule #2-If all but one bus neighboring an observable bus without injection are themselves observable, then all the neighboring buses are observable

7. Rule #3-If all the buses neighboring a bus without injection are observable, then that bus is also observable

8. Different Applications  Different Placement

9. Why Full Observability? • Placing PMUs for full observability covers almost all applications • Starting deployment based on a minimal placement set will reduce the number of PMUs  save money

10. Comprehensive Strategy • Placement Model • What is considered a bus or branch for observability • What model to start from • Placement Algorithm • Which algorithm to choose • Implementation Schedule • Order in which PMU installation

11. Placement Model • Buses • Physical limitations • Necessary buses • Voltage Range • Branches • Carry a variable current between two buses • Injection • Variable injection that is needed

12. Buses • Substation Superbus-used the most

13. Buses • Tapped Lines

14. Buses • Dummy or False buses

15. Placement Model • Buses • Physical limitations • Necessary buses • Voltage Range • Branches • Carry a continual current between two buses • Injection • Variable injection that is needed

16. Branches • Transformers

17. Branches • DC Lines

18. Placement Model • Buses • Physical limitations • Necessary buses • Voltage Range • Branches • Connect buses, but how do I say the criteria that rules out DC lines • Injection • Variable injection that is required for full observability

19. Injection • Switched Shunts (4.3)

20. Results of India reduction

21. Comprehensive Strategy • Placement Model • What is considered a bus or branch for observability • What model to start from • Placement Algorithm • Which algorithm to choose • Implementation Schedule • Order in which PMU installation

22. Goals of Placement Algorithm • Smallest minimal placement set • Each installed PMU can cost up to $55k • Placement on certain buses

23. Placement Algorithm Complexity and NP of transmission systems unknown if there is an optimal solution For this reason approximation algorithms should: be fast and perhaps varied results (talk of local minima)

24. Greedy Algorithms • Iterative approximation algorithm that chooses one item at a time based on a greedy choice property. • Greedy choice property=linked unobserved buses

25. Simple Greedy Algorithm-IEEE 14 Bus Example

30. Randomized Greedy Algorithm • For every iteration, compare greedy candidate bus with candidate buses chosen at random

31. Randomized Greedy Algorithm-IEEE 14 Bus Example

34. India Results • Run Time ~ 17 min • Smallest set = 76PMU. PMUs required on 22% of system buses • At least 20 different placement sets of size 76 • Found results that varied from 76-79 PMU • Success rate = 17%

35. Run Time (sec) System Size (buses)

36. Other considerations • Bus weight • PMUs already installed • Easy to implement

37. Comprehensive Strategy • Placement Model • What is considered a bus or branch for observability • What model to start from • Placement Algorithm • Which algorithm to choose • Implementation Schedule • Order in which PMU installation

38. Phased Installation • Incrementally increase observability • Needs a metric to measure observability

39. Depth of Unobservability • Nuqui’sdefinition – placing a PMU every ith bus along a spanning tree insures a minimal DOU • Definition is unclear when not using spanning trees

40. My Definition • Based on Path Length to 2 observed buses where i and j are observed from different PMUs

41. IEEE 14 Bus SystemDepth of 5 Unobservability

42. Advantages of my definition • Consistent with Nuqui’s-bounded • Works with any algorithm • Easy to calculate

43. Phased Installation Algorithm • Greedy Algorithm with DOUbus as greedy value • Place PMUs from placement set one at a time

44. Summary • Placement for full observability • Placement Model • Placement Algorithms • Phased Installation

45. My Contributions • Define and advocate integrated approach • Defining Placement Model, Reduction Rules, Reduction Program • Assisting Nicolas De Olivera with Development of Randomized Greedy Algorithm • Practical DOU Definition

46. Future Work • Further test and validate/improve the reduction rules and DOU definition. • Apply the basic principles of this strategy to other topics relating to placing equipment in transmission systems. • Test how phasor estimates affect a PMU sets performance for incomplete observability

47. Encouragement from my advisor • “relax, get some sleep the night before, and you’ll probably be OK” • “besides you have an easy committee”