Dealing with two time scales in distribution system state ...abur/ieee/PES2013/Paper1.pdf · DEALING(WITH(TWO(TIME(SCALES(IN(DISTRIBUTION(SYSTEMSTATE(ESTIMATORS! ... • Very!few!RTU

DEALING WITH TWO TIME SCALES IN DISTRIBUTION SYSTEM STATE ESTIMATORS

Panel session State Es(ma(on for Distribu(on Opera(ons: sharing the experiences of implementa(on, usage and complexi(es

A. Gómez-‐Expósito C. Gómez-‐Quiles University of Seville

Spain

I. Dzafic Siemens AG Germany

IEEE/PES General Mee(ng, Vancouver July 25, 2013

CONTENTS

•  Mo(va(on •  Distribu(on-‐level informa(on •  State Es(ma(on with two (me scales •  Preliminary results •  Conclusions

© A. Gómez-‐Expósito, 2013

Telemetered informa(on in today’s distribu(on substa(ons

Feeder head currents

Bus voltage magnitudes

MOTIVATION


MOTIVATION

The consequence is...

Feeder head currents

Bus voltage magnitudes

MV & LV feeder system is literally a

BLACK BOX


MOTIVATION

Is it sa(sfactory?

Passive loads Planning criteria are sufficient


MOTIVATION

Is it sa(sfactory?

?

Ac(ve loads

?

?

?

Need to check (in real-‐(me): -‐  Overvoltages -‐  Undervoltages -‐  Feeder conges(ons -‐  Islanding, etc.


MOTIVATION

What can we do to improve drama(cally the situa(on?

Use AMI/AMR data to “illuminate” the MV radial system

Smart grid paradigm


DistribuKon-‐level informaKon

•  SCADA & DMS •  Feeder automa(on devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators)

Several (heterogeneous) informa(on sources in upcoming Smart Grids:




•  Very few RTU measurements captured at HV-‐MV substa(ons

•  Sampled every few seconds



•  SCADA & DMS •  Feeder automaKon devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators)

•  Intermediate switching points for fault management

•  Can be used as addi(onal telemeasured points (RTUs)


Example of feeder automaKon devices Siemens Feeder Automa(on controller: SIPROTEC 7SC80

Can be used both as fault locator and RTU (V, I, P, Q, cos ϕ)


•  SCADA & DMS •  Feeder automa(on devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators) Depending on specific regula(on:

•  Day-‐ahead hourly forecas(ng of energy produc(on

•  Real produc(on periodically submiged to DMS



•  SCADA & DMS •  Distribu(on automa(on devices •  Distributed generators •  Historic load paUerns/profiles •  AMI data (Smart Meters concentrators) •  Day-‐ahead hourly load forecas(ng

•  Assumed PF for typical loads -‐ Hourly values of P&Q



•  SCADA & DMS •  Distribu(on automa(on devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators)

•  Involves DMS-‐AMI communica(ons •  Depending on bandwidth availability: -‐ From 15’ to 24h snapshot latency


Two different latencies


•  Snapshots updated from few sec. to about a minute

•  Insufficient to assure network observability



•  SCADA •  Feeder automa(on devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators)

•  Snapshots updated from 15’ to 24h •  Barely cri(cal informa(on to assure

network observability © A. Gómez-‐Expósito, 2013


•  SCADA •  Feeder automa(on devices •  Distributed generators •  Historic load pagerns/profiles •  AMI data (Smart Meters concentrators)

Minimum redundancy levels obtained only when both informa(on types are properly combined


State EsKmaKon with two measurement latencies

Two dis(nct sets of measurements, captured at different rates:

t

zp,j zp,j+1

zr,k

Real-time incomplete information system (fast rate)

Pseudomeasurements: less accurate, “complete” information system (slow rate)

zr,k+1

!T = nTk

kT


zp,j

zp,j+1

zr,k

Accuracy of Zp,j depends on the rate of change of loads

zr,k+1

Load evolu(on

More accurate Less accurate



Accuracy of Zp,j depends on the rate of change of loads


zp,j

zp,j+1

Load evolu(on

λ: Rate of load change between two consecu(ve slow snapshots


MathemaKcal model: WLS es(ma(on with zp and zr

⎥⎦

⎤⎢⎣

⎡+⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

r

p

r

p

r

p

xhxh

zz

ε

ε

)()(


Gauss-‐Newton methodology (Normal equa(ons): where

( ) ( ) ( ))()( xhzWHxhzWHxHWHHWH rrrtrppp

tprr

trpp

tp −+−=Δ+

cov(!p ) =Wp

!1 cov(!r ) =Wr

!1


•  First (cold) execuKon: both zp and zr updated


t

zp,j zp,j+1

zr,j

Base-‐case load: P & Q


•  n-‐1 “warm” execuKons: only zr updated


t

zr,k

zp,j zp,j+1


Latest es(mate used to start itera(ons © A. Gómez-‐Expósito, 2013

•  n-‐1 “warm” execuKons: only zr updated


t

zr,k

zp,j zp,j+1


Final load: λ(P & Q)

Latest es(mate used to start itera(ons © A. Gómez-‐Expósito, 2013

Case study

Can a small subset of “real-‐(me” measurements,

when combined with a cri(cal set of (outdated)

pseudomeasurements, provide accurate enough

es(mates ? (reconstruc(on of network state)


Case study

•  Small radial distribu(on system (20 buses)

•  Pseudomeasurements (zp): V1 and P & Q at all buses

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Nx= Nzp = 39


Case study



•  Real-‐Kme measurements (zr): I & V 2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Current flow at branch 1-‐2

Voltage mag. at node 5

Nx= Nzp = 39

Nzr = 5

Redundancy = 1.128

•  Very few in prac(ce •  In our tests limited to:


Case study



•  Different scenarios for real-‐Kme measurements (zr): •  Measurement type: I & V •  Measurement loca(ons •  Rate of load change: λmax=1.5 •  Change in power flow direc(on

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Current flow at branch 1-‐2

Voltage mag. at node 5


Case study



•  Different scenarios for real-‐Kme measurements (zr): •  Measurement type: I & V •  Measurement loca(ons •  Rate of load change: λmax=1.5 •  Change in power flow direc(on

•  WLS solu(ons compared with exact state: •  zp values “frozen” with base-‐case load •  zr values updated according to load evolu(on

[1< λ<1.5 ; ∆λ=0.05]


-‐ A -‐ zr = currents

-‐ B -‐ zr = voltages

Test 1: Comparison of measurement type: I versus V

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

Set zr: uniformly distributed sets of measurements

-‐  Current meas. beger than voltage meas. (up to 10 (mes lower voltage error) -‐  Errors increase linearly with load growth (pseudomeasurement obsolescence)

0,0E+00

2,0E-‐03

4,0E-‐03

6,0E-‐03

8,0E-‐03

1,0E-‐02

1,2E-‐02

1,1 1,2 1,3 1,4 1,5

A) Average errors

B) Average errors

A) Maximum errors

B) Maximum errors

λ

|Viwls !Vi

exact |


-‐ A -‐ zr uniform

-‐ C -‐ zr at the ends

Test 2: Comparison of measurement loca(on

Sets zr: current measurements, different loca(ons

-‐  Beger results with uniformly distributed current measurements

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

λ

0,0E+00

2,0E-‐04

4,0E-‐04

6,0E-‐04

8,0E-‐04

1,0E-‐03

1,2E-‐03

1,4E-‐03

1,6E-‐03

1,1 1,2 1,3 1,4 1,5

A) Average errors

C) Average errors

A) Maximum errors

C) Maximum errors

|Viwls !Vi

exact |Voltage errors





-‐  Beger results with uniformly distributed current measurements

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

λ

0,0E+00

1,0E-‐01

2,0E-‐01

3,0E-‐01

4,0E-‐01

5,0E-‐01

6,0E-‐01

7,0E-‐01

8,0E-‐01

1,1 1,2 1,3 1,4 1,5

A) Average errors

C) Average errors

A) Maximum errors

C) Maximum errors

Sets zr: current measurements, different loca(ons

| Siwls ! Si

exact |Injec(on errors



1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

16

18

20

Sij (p

er u

nit,

Sba

se=1

00kV

A)

Branch i-j

λ = 1.1

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e er

ror (

per u

nit)

Relative errorLoad FlowWLS SE

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

16

18

20

Sij (p

er u

nit,

Sba

se=1

00kV

A)

Branch i-j

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e er

ror (

per u

nit)




2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Branch power flows



1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

16

18

20

Sij (p

er u

nit,

Sba

se=1

00kV

A)

Branch i-j

λ = 1.5

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e er

ror (

per u

nit)


1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

16

18

20

Sij (p

er u

nit,

Sba

se=1

00kV

A)

Branch i-j

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e er

ror (

per u

nit)




2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Branch power flows


-‐ A -‐

Test 3: Weigh(ng coefficient influence

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

Set zr: current measurements, uniformly distributed

0,0E+00

2,0E-‐04

4,0E-‐04

6,0E-‐04

8,0E-‐04

1,0E-‐03

1,2E-‐03

1,1 1,2 1,3 1,4 1,5

A) Average errors

D) Average errors

A) Maximum errors

D) Maximum errors

λ

σp = 0.1

σr = 0.1 σp = 0.1

σr = 0.001

-‐  Similar results with equal or different weights

-‐ D -‐

|Viwls !Vi



Test 4: Influence of head current

-‐ A -‐ With I12

-‐ E -‐ Without I12

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78

Same redundancy

-‐  Beger results with head current measurement

λ

0,0E+00

2,0E-‐04

4,0E-‐04

6,0E-‐04

8,0E-‐04

1,0E-‐03

1,2E-‐03

1,4E-‐03

1,1 1,2 1,3 1,4 1,5

A) Average errors

E) Average errors

A) Maximum errors

E) Maximum errors

|Viwls !Vi



Test 5: Change in power flow direc(on (distributed genera(on)

Scenario: Power injec(on changes from P12 to -‐P12 while rest of loads increase from λ=1 up to λ=1.5.

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Set zr: currents at the end of feeder laterals


2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.05

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.1

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.15

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.2

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.25

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.3

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.35

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.4

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.45

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.5

LF SWLS S

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78


-‐  Inability of current measurements to track sign changes in P


-‐  Same happens when Q12 changes its sign

-‐ C’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78

Set zr: Ac(ve power flow measurements ‘ ’ instead of currents


Scenario: Power injec(on changes from P12 to -‐P12 while rest of loads increase from λ=1 up to λ=1.5.


-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.05

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.1

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.15

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.2

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.25

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.3

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.35

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.4

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.45

LF SWLS S



-‐ F’ -‐

2 3 4 5

1

6 7 8 9 10 11 12

17

18 19 20 21 22

23

78 2 3 4 5 6 7 8 9 10 11 12 17 18 19 20 21 22 23 78

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

P (p

er u

nit,

Sbas

e=10

0kVA

)

Node number

λ = 1.5

LF SWLS S

-‐  Ac(ve power flow measurements detect power flow inversion



Conclusions

•  Smart grid context: new “real-‐(me” feeder measurements will become gradually available (fault detec(on & isola(on).

•  Insufficient to achieve observability: need to combine with other informaKon sources (pseudomeasurements): AMI.

•  Two measurement latencies and accuracy levels.

•  Very few Ampere measurements may suffice to provide reasonable es(mates, even for 50% load increase.

•  Inability of Ampere measurements to track counterflows.

•  Power rather than Ampere measurements encouraged in the presence of distributed generaKon.

•  Future efforts: test larger realis(c systems & prac(cal implementa(on (computa(onal saving).


DEALING WITH TWO TIME SCALES IN DISTRIBUTION SYSTEM STATE ESTIMATORS

Panel session State Es(ma(on for Distribu(on Opera(ons: sharing the experiences of implementa(on, usage and complexi(es

A. Gómez-‐Expósito C. Gómez-‐Quiles University of Seville

Spain

I. Dzafic Siemens AG Germany

IEEE/PES General Mee(ng, Vancouver July 25, 2013

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-‐A-‐ zr current meas.

-‐G-‐ zr ac(ve power meas.

Test 7: current measurements versus ac(ve power measurements


-‐G-‐ zr ac(ve power meas.

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

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S ij (per

uni

t, Sb

ase=

100k

VA)

Branch i-j

λ = 1.5

0

0.05

0.1

0.15

0.2

0.25

Rela

tive

erro

r (pe

r uni

t)

Rel.errorLF SWLS S

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

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P ij (per

uni

t, Sb

ase=

100k

VA)

Branch i-j

λ = 1.5

0

0.05

0.1

0.15

0.2

0.25

Rela

tive

erro

r (pe

r uni

t)

Rel.errorLF SWLS S

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6 7 8 9 10 11 12

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18 19 20 21 22

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78


-‐A-‐ zr current meas.

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

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18

20

P ij (per

uni

t, Sb

ase=

100k

VA)

Branch i-j

λ = 1.5

0

0.05

0.1

0.15

0.2

0.25

Rela

tive

erro

r (pe

r uni

t)

Rel.errorLF SWLS S

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 3-17 5-18 18-19 19-20 20-21 21-22 19-23 10-780

2

4

6

8

10

12

14

16

18

20

S ij (per

uni

t, Sb

ase=

100k

VA)

Branch i-j

λ = 1.5

0

0.05

0.1

0.15

0.2

0.25

Rela

tive

erro

r (pe

r uni

t)

Rel.errorLF SWLS S

2 3 4 5

1

6 7 8 9

10 11 12

17

18 19 20 21 22

23

78


Documents

Dealing with two time scales in distribution system state ...abur/ieee/PES2013/Paper1.pdf · DEALING(WITH(TWO(TIME(SCALES(IN(DISTRIBUTION(SYSTEMSTATE(ESTIMATORS! ... • Very!few!RTU