Hierarchical State Estimation Using Phasor Measurement Units

Transcription

1 Herarchcal State Estmaton Usng Phasor Measurement Unts Al Abur Northeastern Unversty Benny Zhao (CA-ISO) and Yeo-Jun Yoon (KPX) IEEE PES GM, Calgary, Canada State Estmaton Workng Group Meetng July 28, 2009

2 Mult-area Operaton P L P G Independent System Operator

3 Challenge: How to montor the system state? Centralzed / Flat Soluton: Data ntensve. Dmenson grows wth system sze (areas). Data base/format must be standardzed. Large amounts of data and measurements must be exchanged between areas and ISO. Vulnerable to dsturbances to the central or any one of the area SCADA systems.

4 Challenge: How to montor the system state? Herarchcal Soluton: Each area uses ts own data. Problem sze does not grow sgnfcantly wth number of areas. Each area has ts own SE and Data-base. Lmted number of data and measurements must be exchanged between areas and ISO. Partal system montorng s possble durng ndvdual area falures.

5 Problem Statement and Constrants Areas are reluctant to share network data and measurements due to competton. Overall system state must be estmated based on lmted measurements from each area. Gross errors (bad data) n measurements must be detected, dentfed and corrected even f they appear at the area boundares. If the entre system s not observable, all states assocated wth the observable slands wll have to be estmated.

6 State Estmaton Problem Mnmze J ( x) = r T R 1 r Subject to z = h( x) + r R s the covarance of measurement errors. h(x) s the estmated value of z. x s the estmated state vector.

7 Herarchcal State Estmaton Each area SE estmates ts own state. Coordnator SE merges the solutons, and processes bad data for boundary measurements. Coordnator SE Area 1 SE Area 2 SE Area L SE

8 Measurement Decomposton k Boundary m P k : unusable P m : unusable P km : unusable P mk : unusable area 1 k m area 2 P k : unusable by 2 P m : unusable by 1 May not be avalable to area 2. May not be avalable to area 1.

9 Proposed Decomposton Area 1 Internal bus Area 3 Boundary bus External bus Area 2

10 Proposed Decomposton Defne the state vector for each area : X nt Area X ext X = X X X nt b ext X b

11 Proposed Decomposton Measurement vector for each area : Area Z c Z p Z c Z Unusable Measurements Z = c Z p Conventonal Measurements p Z Phasor (PMU) Measurements

12 Propertes of z Should render an observable area. External boundary buses may or may not be observable. Redundancy must be suffcent to make the nternal bad data detectable and dentfable. Else, employ optmal meter placement [1] methods to address ths problem. [1] Magnago, F.H. and Abur, A., "Unfed Approach to Robust Meter Placement aganst Bad Data and Branch Outages, IEEE Trans. on Power Systems, Vol.15, No.3, August 2000, pp

13 Area State Estmaton Mnmze Subject to where: e N(0, σ 2) j j m : number of measurements n z z ˆ = h (ˆ x) estmated measurement j j x ˆ ˆ nt x = xˆ estmated state b xˆ ext m 1 ( r )2 j = 1 σ 2 j j z = h (ˆ x) + r j j j 1 j m

14 Measurements Receved and Used by the Coordnator s SE Each area state estmates are treated as pseudomeasurements wth the followng dstrbuton: N( xˆ, Λ ) where : Λ G [ ] 1 = G [ ] T [ ] 1[ ] = H R H [ H ] = h / x R jk = j cov( e ) k

15 Boundary measurements from each area Z b. Any avalable PMU measurements from area, Z p. Network data at area boundares. Boundary Meas. PMU Te-lnes + Frst ter nternal lnes

16 Coordnator s SE Mnmze k j = 1 1 R jj ( r )2 j e j Subject to z = h (ˆ x ) + r j j b j 1 j k N(0, σ 2 ) boundary measurements j N(0, σ 2 ) PMU measurements pj N(0, Λ ) area state estmates jj

17 = = = L p z p z L b z b z L x x x j Z L b x b x b X j e dag jj R 1 1 ˆ 2 ˆ 1 ˆ 1 )} {cov( Note: Multple pseudo-measurements for the boundary states. k m 1 2 ˆ2, ˆ1 ˆ2, ˆ1, x m x m k x k x

18 Propertes No boundary measurements are dscarded. All detectable / dentfable bad data are detected and dentfed. PMU measurements are effectvely used, but not requred for ths scheme to work. Areas do not share network data (nternal system detals) or ntermedate teraton results. They only provde boundary network model and measurements and ther estmated states.

19 IEEE 14 Bus System : Two Area Example

20 COORDINATOR AREA 2 AREA 1

21 Estmaton Results wth Gaussan errors (No Bad Data) -Measurements- Inj. Flow Volt.Mag Phase I-real I-mag Boundary External Integrated Area Area Coordnator Error S.D Computed Computed -Estmaton Results- Degrees of Freedom Ch- Square lmt Objectve functon J(x) Largest Normalzed Resdual Integrated Area Area Coordnator

22 Bad Data Processng (P nj at Bus 6) Note that P 6 becomes crtcal after decomposton. Bad data can not be detected by the SE of area 2.

23 Bad Data Identfcaton Results Area 2 SE Ch-square lmt (0.99% ) Objectve functon J(x) Measurement Type Largest Normalzed Resdual I-real (9,10) I-mag (9,7) I-real (9,14) Coordnator SE Ch-square lmt (0.99% ) Objectve functon J(x) Measurement Type Largest Normalzed Resdual Pnj (6) I-real (5,6) Qnj (6)

24 Conclusons A herarchcal state estmaton approach s proposed. The man advantage of the proposed set up s that ndvdual area state estmators can operate ndependently and do not have to share network data or measurements wth any neghbors. Coordnaton s accomplshed va a central coordnator, such as an ISO, whch receves state estmaton solutons from ndvdual areas and coordnates them.

25 Conclusons... Coordnator also carres out bad data processng functon n order to detect mssed bad data by ndvdual area estmators due to the reduced redundancy at area boundares durng ndvdual area estmatons. Havng PMU measurements greatly facltates but are not requred for the herarchcal soluton.