Optimal Placement of Phasor Measurement Units for State Estimation (Project S-23G) S

Transcription

1 Optimal Placement o Phasor Measurement Units or State Estimation (Project S-3G) S Ali Abur Northeastern University (Project was completed at TAMU) Final Reports Tele-seminar November, :-3: p.m. Eastern Time 5 Ali Abur.. All rights reserved.

2 Outline Introduction Motivation and Objectives Problem Statement and Formulation Proposed Solution Case Studies Impact on Bad Data Processing Impact on SE Accuracy Conclusions

3 Introduction State estimators acilitate on-line monitoring o power systems. Available measurements have traditionally ecluded phase angle (phasor) measurements. Phasor measurement units (PMU) are devices, which use synchronization signals rom the global positioning system (GPS) satellites and provide the phasors o voltage and currents measured at a given substation. 3

4 Motivation TVA is in the process o installing PMUs or enhanced monitoring o the TVA system and wishes to determine the optimal locations or them.

5 Project Objectives Make use o a minimum number o PMUs in order to make the system ully observable. Since installation o PMUs will be a gradual process, determine the best possible locations or a limited number o PMUs at the beginning. Develop a systematic method or inding the best locations or new PMUs in the presence o other already placed PMUs and/or conventional measurements. 5

6 Preliminary Observations PMUs typically have higher accuracy than conventional measurements, however their accuracy will be reduced due to the instrument transormers used at their inputs. They are useul or other applications such as system protection, control and stability assessment. May aid topology error identiication, parameter error detection and correction. May improve state estimation, subsequently improving market unctions (e.g. LMP). 6

7 Secondary Objectives Determine strategies o placing PMUs in order to also improve bad data processing. Study the impact o PMUs on the accuracy o state estimation. Speciically, address the questions: Do more PMUs translate into more accuracy? Is there a trade o between incremental increase in accuracy and investments in PMUs? How do we quantiy and value SE accuracy?

8 PMU Placement Problem Assumption: A PMU placed at a bus makes that bus and all its neighbors observable. I the number o PMU channels is not suicient, then this assumption will be relaed. I phasors PMU V phasor 8

9 Approach: PMU Placement Problem Set up an integer programming problem where all the system buses are made observable by placing PMUs at a minimum number o buses throughout the system. I there are PMUs already installed or planned to be installed at speciic buses, start with these already pre- assigned to their respective buses. I there are zero injection buses, incorporate this inormation into the placement logic and save as many PMUs as possible. 9

10 PMU Placement Problem minimize subject to n w i i i ( X ) ˆ i i a PMU is installed otherwise at bus i

11 Illustrative Eample Illustrative Eample otherwise i and m are connected k i m k i k,m A A ) ( X A X

12 Handling Injections Handling Injections A 6' 6' 5 5 6' 5 6' ) ( X

13 Eects o considering zero injections Systems No. o zero injections Number o PMUs Ignoring zero Injections Using zero injections -bus 3 5-bus 5 8-bus 3 9 3

14 Illustrative Eample Only 3 PMUs make the entire system observable. Note that bus is a zero injection bus.

15 5 5 Handling Flows Handling Flows 6' _ 6' new 6' 6 6' 5 5 6' 5 6' _ ) ( new X

16 Use o eisting lows Meas. set no. Flow measurements in the set System 8-bus Flow measurement set none and, and 3 Number o PMUs

17 Placement against the loss o a single PMU Choose two independent PMU sets, a primary set and a backup set, each o which can make the system observable on its own. I any o the PMUs is lost, the alternative set o PMUs will guarantee network observability. Choose the backup set by removing all the i terms in the constraint unctions, where bus i is in the primary set.

18 Eects o considering loss o single PMUs Systems No. o zero injections Number o PMUs Ignoring zero injections Using zero injections -bus 9 5-bus bus 66 8

19 TVA s s Network A prototype PMU placement program is developed. Four cases are studied: No installed PMUs eisting PMUs 3 eisting and planned PMUs No installed PMUs but considering 33 zero injection buses 9

20 Case Results Total no. o buses 35 No. o zero injection buses 33 Required PMUs Case : No installed PMUs 3 Case : Eisting PMUs () 38 Case 3: Eisting and planned PMUs (3) 39 New PMUs Case : No installed PMUs but considering zero-injection buses 95 95

21 How can PMUs help to improve Bad Data Detection? A measurement is said to be critical i the system becomes unobservable upon its removal. Bad data appearing in critical measurements can NOT be detected. Adding new measurements at strategic locations will transorm them, allowing detection o bad data which would otherwise have been missed.

22 Transorming Critical Measurements Critical Meas. Type F-3 3 P F F- F-56 5 I- 6 I- I-39 8 I-3 9 I-6 P I-8 I-56 I-5 3 I-33

23 Eect o PMUs on SE Accuracy I PMUs are more accurate than all other conventional meters, then estimation error variances or system states are epected to be reduced. Other application unctions, such as LMP calculations will be carried out with higher accuracy when the state estimates are more accurately obtained. 3

24 Quantiying Accuracy G cov( ˆ ) D G D ii σ eˆ D d d G O d 88 d. 99

25 Eect o PMU on Accuracy o State Estimation % No PMU %PMU PMU 3%PMU %PMU Only PMUs Power Injections Power Flows Voltage magnitude PMU ( v, 3 currents ) PMU Eample- PMU PMU Measurement Voltage 3 Currents --Measurement Measurement-- Power Injection Power Flow 5

26 Simulation Results or IEEE 3Bus-System: 6

27 Simulation Results or IEEE 3Bus-System:

28 Conclusions In the absence o any other measurements, power systems can be made observable by placing PMUs at roughly 3% o the buses in the system. This number may signiicantly decrease i there are zero injection buses. This number will increase i loss o PMUs is taken into account or reliability. 8

29 Conclusions... Accuracy o state estimation can be improved by strategically placing PMUs at % o the network buses.. Increasing the number o PMUs urther will not be as eective. Placing ew PMUs can transorm several critical measurements, allowing their gross errors to be detectable. 9