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 Observability refers 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 propertylinked unobserved buses

25
Simple Greedy Algorithm-IEEE 14 Bus Example
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
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
32
(No Transcript)
33
(No Transcript)
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

• Nuquis definition 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 Nuquis-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
  youll probably be OK
• besides you have an easy committee