Dynamic Line Rating State Estimation Ph.D. Defense
David L. Alvarez A. Ph.D. Candidate
[email protected] December 5, 2017 Supervisor: Co-Adviser:
Prof. Javier A. Rosero, Ph.D. Prof. Enrique E. Mombello, Ph.D.
Dissertation Committee: Prof. Mario A. R´ıos, Ph.D., U. Andes, Bogot´ a Prof. Oscar G. Duarte, Ph.D., UNAL, Bogot´ a Prof. Alejandro Garc´ es, Ph.D., UTP, Pereira Prof. Ernesto P´ erez, Ph.D., UNAL, Medellin
Outline DLR State Estimation David L. Alvarez A. Introduction Objective
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
State Estimation Assessment of Algorithms Conclusions
:
58
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
1. DLR Methods
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
5. Conclusions
Modern power systems - New challenges Transformers, cables, and OHL are closer to their operate limits DLR State Estimation David L. Alvarez A.
G G
Introduction 1
Motivation Literature Review
Objective State Estimation Assessment of Algorithms
G
Conclusions
CIGRE - Study Committees
:
58
Technologies to Increase OHL’s Capacity Relative cost and ability according to CIGRE-425
Introduction 2
Motivation Literature Review
Objective State Estimation Assessment of Algorithms Conclusions
:
58
B2-C1 (19). Increasing Capacity of Overhead Transmission Lines: Needs and Solutions. CIGRE, 2010
David L. Alvarez A.
Conseil International des grands r´eseaux ´electriques. Joint working group
DLR State Estimation
SLR vs DLR Smart grid, real time monitoring DLR State Estimation
i [pu]
David L. Alvarez A.
G
DLR
2
G
Introduction
SLR
3
Motivation Literature Review
1
Objective
0
State Estimation
t
G
Assessment of Algorithms
Dynamic Line Rating (DLR) or Real Time Thermal Rating (RTTR)
Conclusions
It is defined by the CIGRE as “the thermal rating calculated based on real-time weather data”.
Electrical and thermal states Adiabatic ms
s
Electromagnetic Transient :
58
Unsteady State
min
Electro-mechanic Transient
Steady State
h
Steady State
DLR Applications Operation and control of power systems DLR State Estimation Operation and Planning
David L. Alvarez A. Introduction 4
Motivation Literature Review
Day-ahead Short-Term Operation Planning Planning Safe, Economical, Maintenance
Operation
Objective Contingencies
State Estimation Assessment of Algorithms
Long-Term Planning Expansion
Rating
Conclusions
DLR SLR
Overloading Acceptable Range Overloading Acceptable Range Normal Operation Normal Operation
:
58
Normal
Alert
Emergency
In Extremis
Restauration
Dynamic Line Rating (DLR) CIGRE 498 Clasification DLR State Estimation
Real Time Monitoring RTM 30
David L. Alvarez A. 25
Introduction
Stability
Motivation
Thermal
Sag
Tension
20
5 y [m]
Literature Review
Mechanical DLR
Objective
Temperature
15
o
T =10 [ C]
10
T =20 [oC]
State Estimation
T =30 [oC] o
T =40 [ C] T =50 [oC]
5
Assessment of Algorithms
T =60 [oC] o
T =70 [ C] T =80 [oC] 0
Indirect Measurement
Conclusions
Direct Measurement • Angle measurement • Clearance • Wind vibration • DGPS • Temperature • PMU
Weather stations: • Temperature • Wind velocity and angle • Solar radiation
0
200
400
600
800
1000 1200 x [m]
1400
1600
1800
Electro-Magnetic i, v E~
TS , P, σ R, L, C
Average conductor temperature
Rating limit :
58
Thermal ~ Q, Ta , S, ϑ
D, ℓ
Mechanical H
2000
Indirect Measurementes Atmospheric conditions, current intensity and conductor characteristics DLR State Estimation David L. Alvarez A. Introduction
Thermal transient
Motivation Literature Review
6
Objective
dTS
Solar Radiation - S
dt
State Estimation
=
QJ (TS ) + QS − QC (TS ) − QR (TS ) mc c
Current - |ikm |
Assessment of Algorithms
~ Wind - ϑ
Thermal equilibrium
Conclusions
QJ + QS = QC + QR
7
2 6.5
1 6
°
64.5 N
64.5° N 0
5.5
-1
5
Numerical integration
4.5
-2
4
-3 3.5
-4 3
-5 2.5
-6 2
21.5° W
:
58
21.5° W
∆TS =
QJ (TS ) + QS − QC (TS ) − QR (TS ) mc c
∆t
Direct Measurements - Tension Forces that act on an OHL DLR State Estimation
y
David L. Alvarez A. Introduction Motivation Literature Review
7
y=
Fx cosh mc g
mc gx Fx
!
Objective
Fy + dFy dl
State Estimation
Fx F~
Assessment of Algorithms x
Conclusions
dl
F~ + d F~ Fx + dFx
mc g Fy
State equation, H = Fx # " EA (Rs mc g )2 EA (Rs mc g )2 2 + EAεt (TS − Tref ) = HS HS − HTref + 24 24HTref 2
:
58
Tensioning Section DLR State Estimation
30
David L. Alvarez A. 25
Introduction Motivation Literature Review
20
8
y [m]
Objective State Estimation Assessment of Algorithms
15
T =10 [oC]
10
T =20 [oC] T =30 [oC]
Conclusions
T =40 [oC] T =50 [oC]
5
T =60 [oC] o
T =70 [ C] T =80 [oC] 0
0
200
400
600
800
1000 1200 x [m]
1400
Ruling Span Approximation Rs = :
58
sP
n
si3 i =1 si
Pin=1
1600
1800
2000
Direct Measurements - Sag Sag-Tension Method DLR State Estimation
y
David L. Alvarez A.
s
A
Introduction Motivation Literature Review
h
9
Objective
f
State Estimation
D
Assessment of Algorithms
B
Conclusions
H mc g x 0
Catenary Equation " H D= cosh mc g :
58
mc gs 2H
!
#
−1
Synchrophasor Measurements Relationship between resistivity and temperature DLR State Estimation
R(TS , ℓ)
ik
David L. Alvarez A.
im +
1 C (D, ℓ) 2
vk
Introduction Motivation Literature Review
L(ℓ)
+
10 90
120 30
0
180
0
270
GPS
30
210
300
330 240
TS1
TS2
TSn
~a , S T a1 , ϑ 1 1
~a , S T a2 , ϑ 2 2
~a , S T an , ϑ n n
ik = Y
Z ·Y
vk = 58
270
300
i m , vm
Relationship between v , i and Z , Y
:
360
0
i k , vk
Conclusions
60
0
180
330 240
90
150
360
210
Assessment of Algorithms
−
60
150
State Estimation
vm
− 120
Objective
1 C (D, ℓ) 2
4
!
+1
Z ·Y 2
vm − !
+1
Z ·Y 2
!
+1
v m − Z · im
im
OHL under test - BR1 Landsnet Weather interpolation using Biharmonic splines at 2016-04-18 21:00 DLR State Estimation
2
David L. Alvarez A.
1
64.5° N
Introduction
0
Motivation
-1
Literature Review
11 -2
Objective
-3
State Estimation
-4
-5
Assessment of Algorithms
-6
Conclusions
21.5° W
7
6.5
6
64.5° N 5.5
5
4.5
4
3.5
3
2.5
2
:
58
21.5° W
Temperature along the OHL Timestamps of atmospheric conditions each 3 hours DLR State Estimation David L. Alvarez A. Introduction Motivation Literature Review
12
Objective State Estimation Assessment of Algorithms Conclusions
:
58
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
1. DLR Methods
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
5. Conclusions
General Objective DLR State Estimation
To develop a methodology to estimate thermal rating of power OHLs, taking direct and indirect measurements in order to optimize its capacity.
David L. Alvarez A. Introduction Objective
13
State Estimation
OHL ratings
Network data
Assessment of Algorithms
◮ Conductor data ◮ OHL geometry ◮ Configuration
Conclusions
State prediction
State estimation
◮ GIS data
DLR
Downscaling Weather Nowcast
Numerical Weather Prediction - NWP
Indirect Methods :
58
PMU vk , i k , vm , i m
Sag Tension Temperature
Direct Methods
Methodology of the Dissertation DLR State Estimation
1. DLR Methods
David L. Alvarez A. Introduction Objective
14
State Estimation Assessment of Algorithms
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
Conclusions
5. Conclusions :
58
Weighted Least Square Method ε = h (z, ˆx) DLR State Estimation
Least Squared Error Norm
David L. Alvarez A. Introduction Objective
|ε|2 = 15
Nm X
wn hn (z, ˆ x)2 = [h(z, ˆ x)]T [W] [h(z, ˆ x)]
n=1
State Estimation
Cost function
Assessment of Algorithms
min J (x) = [h(z, ˆ x)]T [W] [h(z, ˆ x)]
Conclusions
x
∂J (x)/∂x = 0, or the gradient ∇x J (x) = 0 ∇x J (x) = [H]T [W] [h(z, ˆ x)]
Iterative Newton’s method :
58
h i−1 ∆ˆ x = [H]T [W] [H] [H]T [W] [h(z, ˆ x)]
Hybrid Extended Kalman Filter - EKF To Model, predict and update DLR State Estimation David L. Alvarez A. Introduction Objective
zk = xk + vk
⊗
16
Pˆk+
State Estimation
Pˆk−
Assessment of Algorithms
xˆk+
− xˆk+1
xˆk−
Conclusions
+ xˆk−1
t :
58
Contribution to Knowledge DLR state estimation DLR State Estimation David L. Alvarez A. Introduction Objective
DLR State Estimation
17
State Estimation Assessment of Algorithms Conclusions
Affine Arithmetic
Monte Carlo
Weighted least squares
Extended Kalman filter
Atmospheric measurements
Atmospheric measurements
Atmospheric and direct measurements
Atmospheric and direct measurements
Contributions of the thesis
Antonio Piccolo, Alfredo Vaccaro, and Domenico Villacci. Thermal rating assessment of overhead lines by Affine Arithmetic.
:
58
Electric Power Systems Research, 71(3):275–283, 2004 A Michiorri, P C Taylor, and S C E Jupe. Overhead line realtime rating estimation algorithm : description and validation. Proc. IMechE - J. Power and Energy, 224(A):293–304, jan 2009
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
1. DLR Methods
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
5. Conclusions
Steady State State Estimation problem DLR State Estimation
e
OHL data
Introduction Objective
ˆ x= R
L
WLS TS1 TS2
C
z
State Estimation
e
18
Steady State
State estimation
◮ Conductor properties ◮ OHL geometry ◮ Configuration ◮ GIS data
David L. Alvarez A.
· · · TSN
T
z e
Dynamic State
Assessment of Algorithms
Down scaling
NWP
Conclusions
PMU vk , ik , vm , im
Temperature - TS Tension - H Sag - D Direct Methods
Indirect Methods
Integration equations 0=R−
N X n=1
:
58
ℓn Rn′ T
ref
(1 + αn (TSn − Tref ))
2 N 2 X v Y vk Yc m c Rn (TSn ) − im 0 = ik − R − 2 2 n=1
Measurement Model 0 = h (z, x) + e DLR State Estimation
State Variables
David L. Alvarez A.
x= R
Introduction Objective State Estimation 19
Steady State Dynamic State
Assessment of Algorithms
L C
TS1
TS2
· · · TSN
Measurements z = Re (vk ) Im (vk ) Re (ik ) Im (ik ) Re (vm ) . . . Im (vm ) Re (im ) Im (im ) zW zTS zH zD
Conclusions
Residual
ε = h (z, ˆ x) ∇x J (x) = [H]T [W] [h(z, ˆx)] :
T
58
Measurement Functions h (z, x) = Re (hv (z, x)) hR (z, x)
Im (hv (z, x))
hP (z, x)
Re (hi (z, x))
hQ (z, x)
hT (z, x)
DLR State Estimation David L. Alvarez A.
Re (hv (x, z)) = Re (vk ) −
−
Introduction Im (hv (x, z)) = Im (vk ) −
−
Objective Re (hi (x, z)) = Re (ik )−
State Estimation
Im (hi (x, z)) = Im (ik )− −
Dynamic State
Re (vm ) XL YC Im (vm ) YC R Re (vm ) − + Im (im ) XL − Re (im ) R 2 2
hR (z, x) = R −
N X
Rn (TSn )
2 N 2 n=1 X v Y vk Y m Rn (TSn ) − im hP (z, x) = ik − R − 2 2 hQ (z, x) = QC + QR − (QJ + QS )
hT (z, x) = z [TS ] − x [TS ] hH (z, x) = z [H] − H (x [TS ]) hD (z, x) = H (z [D]) − H (x [TS ])
58
! !
Re (vm ) XL YC 2 Im (vm ) YC 2 R Im (im ) XL YC Re (im ) YC R + Re (vm ) YC − + − Im (im ) − 4 4 2 2
n=1
:
!
Re (vm ) YC R Im (vm ) XL YC + Im (vm ) + − Im (im ) R − Re (im ) XL 2 2
Assessment of Algorithms Conclusions
... hD (z, x) T
Im (vm ) XL YC 2 Re (vm ) YC 2 R Re (im ) XL YC Im (im ) YC R − Im (vm ) YC − + − Re (im ) + 4 4 2 2
20
Steady State
Im (hi (z, x)) hH (z, x)
!
Jacobian Matrix H=
∂h(z, x) ∂x
DLR State Estimation David L. Alvarez A.
Introduction Objective State Estimation 21
Steady State Dynamic State
Assessment of Algorithms Conclusions
:
58
H=
∂ Re (hv (z, x)) ∂R ∂ Im (hv (z, x)) ∂R ∂ Re (hi (z, x)) ∂R ∂ Im (hi (z, x)) ∂R ∂hR (z, x) ∂R ∂hE (z, x) ∂R
∂ Re (hv (z, x)) ∂XL ∂ Im (hv (z, x)) ∂XL ∂ Re (hi (z, x)) ∂XL ∂ Im (hi (z, x)) ∂XL
∂ Re (hv (z, x)) ∂YC ∂ Im (hv (z, x)) ∂YC ∂ Re (hi (z, x)) ∂YC ∂ Im (hi (z, x)) ∂YC
0
0
0
∂hE (z, x) ∂YC
0
0
∂hP (z, x) ∂YC
0
0
0
0
0
0
0
0
0
0
0 0 ∂hR (z, x) ∂TS ∂hE (z, x) ∂TS ∂hP (z, x) ∂TS ∂hTS (z, x) ∂TS ∂hH (z, x) ∂TS ∂hD (z, x) ∂TS 0
Weights Matrix - W h W = diag 1/σv 2 1/σh
2
P
1/σv 2 1/σh
1/σi 2
2
Q
1/σi 2
1/σT
2
S
1/σh 2
... iT 1/σh 2
R
1/σH 2
D
DLR State Estimation David L. Alvarez A. Introduction
Standard deviations for σv ,σi , σTS and σH are taking as a third part of the accuracy.
Objective State Estimation 22
Steady State
As remaining measurement functions are taking through indirect measurements the uncertainty is propagated
Dynamic State
Assessment of Algorithms Conclusions
σh(z,x)
:
58
v !2 u u ∂h (z, x) t + = σz1 ∂z1
∂h (z, x) ∂z2
σz2
!2
+ ··· +
∂h (z, x) ∂zN
σzN
!2
Heat Transfer Equation 0 = PCn Tan , Sn , ϑan , TSn + PRn Tan , TSn − DLR State Estimation
2 ! v Y m c − im Ri′ TSn + PSn (Sn ) 2
Forced convective cooling
David L. Alvarez A. Introduction QC = π 2.42 · 10
Objective
−2
+ 7.2 · 10
−5
State Estimation
TS + Ta 2
!!
(TS − Ta ) B1
n
ρr ϑd 1.32 · 10−5 + 9.5 · 10−8
! TS + Ta 2
Solar Radiation - S
Current - |ikm |
~ Wind - ϑ
23
Steady State
Error propagation
Dynamic State
Assessment of Algorithms
σhQ (z,x)
Conclusions
∂QJ ∂ikm ∂QR ∂Ta ∂QC ∂Ta ∂QC ∂ϑ ∂QC ∂δ :
58
v !2 u u ∂QR ∂QC + σTa + σTa =t ∂Ta ∂Ta
∂QC σϑ ∂ϑ
!2
+
∂QC σδ ∂δ
!2
+
∂QJ σi ∂ikm km
′
=2ikm Rref (1 + α (TS − Tref )) = − 4πd ǫσb (Ta + 273)3 ≈ − 2.42 × 10−2 πB1 7.58 × 104 ρr ϑd
n
(A2 + B2 sin δ m1 )
n 2.42 × 10−2 nπ (TS − Ta ) B1 7.58 × 104 ρr ϑd (A2 + B2 sin δ m1 ) ϑ n 2.42 × 10−2 π (TS − Ta ) B1 ≈ 7.58 × 104 ρr ϑd (B2 sin δ m1 m1 cos δ) sin δ
≈
!2
+ σS2
Change State Equation " 0=
EA (Rs mc g)2 24
− Hs 2 Hs − Href +
EA (Rs mc g)2 2
24Href
#
+ EAεt (Ts − Tref )
DLR State Estimation David L. Alvarez A.
Derivative of inverse function
Introduction
y
−1 ′ f (f (H)) =
Objective State Estimation 24
Steady State
TS =
(Rs mc g)2
1
εt 24
H2
Dynamic State
−
1
f ′ (H) F y= cosh ! m g H − HT 1 ref +T − ref 2 HT EAεt x
c
mc gx Fx
!
Fy + dFy dl
Fx F~
ref
x
Assessment of Algorithms Conclusions
Partial derivative dTS dH ∂hH ∂TS
=− =−
(Rs mc g )2 12εt H 3
58
1 EAεt
1 (Rs mc g )2 12εt H 3
:
−
+
1 EAεt
dl mc g Fy
F~ + d F~ Fx + dFx
Catenary Equation " 0=
EA (Rs mc g)2 24
− Hs (D)2 Hs (D) − Href +
EA (Rs mc g)2 24Href
2
+ EAεt (Ts − Tref )
#
DLR State Estimation David L. Alvarez A.
Mechanical tension as a function of sag - Numerical approximation
Introduction
y
Objective State Estimation
h
25
Steady State
s
A
Dynamic State
3
H D−
s 2 mc g H 2 8
−
s 4 (mc g)3 384
f
≈0
D B
Assessment of Algorithms
H mc g x 0
Conclusions Polynomial form - ax 3 + bx 2 + cx + d = 0 2
4
3
a = D , b = −s mc g/8 , c = 0 , d = −s (mc g) /384 H (D) =
r 3
q+
q
q 3 q2 + r − p2 3 + q − q2 + r − p2 3 + p
p=−
:
58
r
b
3a
3
,q = p +
bc − 3ad 6a2
,r =
c
3a
Dynamic Temperature Estimation EKF designed DLR State Estimation
vk u (t)
David L. Alvarez A. Introduction
•
x (t)
Heat transfer Dynamic phenomenon Model
w (t)
Objective State Estimation
ˆ x+ k−1
ˆ+ ˆ˙ − x k−1 , u, 0, t k =f x Prediction
z k = xk + vk •
Measurement process
ˆx− k ˆ+ P k−1
zk
h (xk , vk )
•
ˆ− P k
EKF
⊗
xˆk+
Pˆk+ Pˆk−
− xˆk+1
xˆk−
ˆx+ k ˆ+ P k
• + xˆk−1
Update
Steady State 26
Dynamic State
t
Dynamic state estimation
Assessment of Algorithms
1. Model →
Conclusions
dTS dt
=
QJ (TS ) + QS − QC (TS ) − QR (TS )
f (x, u, w, t) 0 x˙ = 0 0
zk = h (xk , vk ) w (t) ∼ (0, Q) vk ∼ (0, Rk ) :
58
mc c
T x = TS |ϑ| εs αs u = |ikm | Ta δ S z = TS , H, D
Dynamic Temperature Prediction EKF designed DLR State Estimation
vk
David L. Alvarez A.
u (t)
•
x (t)
Heat transfer
Introduction
Dynamic phenomenon Model
w (t)
zk
h (xk , vk )
z k = xk + vk •
Measurement process
⊗
xˆk+
Pˆk+ Pˆk−
− xˆk+1
xˆk−
Objective ˆx− k
State Estimation
ˆ+ P k−1
Steady State
ˆ x+ k−1
ˆ˙ − x x+ k =f ˆ k−1 , u, 0, t Prediction
ˆ− P k
• EKF Update
27
Dynamic State
Assessment of Algorithms
ˆx+ k ˆ+ P k
• + xˆk−1
t
Dynamic state estimation
2. Predict
Conclusions
df dTS F= 0 0
df
df
0
dϑ 0 0 0
dεs 0 0 0
df
df
df
+ f ˆ xk−1 , u, 0, t − 0 ˆ x˙ k = 0 0
+ T T ˙ − = FP+ P k−1 + Pk−1 F + LQL k
:
58
dw ikm L= 0 0 0
dwTa dwδ 0 0 0 0 0 0
dαs 0 0 0 df
df
xˆ,u
dwS 0 0 0 ˆ x,u
Dynamic Temperature Estimation EKF designed DLR State Estimation vk
David L. Alvarez A. u (t)
Introduction
•
Heat transfer Dynamic phenomenon Model
w (t)
Objective
ˆ+ P k−1
Steady State 28
Assessment of Algorithms
ˆ x+ k−1
ˆ˙ − x x+ k =f ˆ k−1 , u, 0, t Prediction
zk
h (xk , vk )
z k = xk + vk •
Measurement process
ˆx− k
State Estimation Dynamic State
x (t)
ˆ− P k
• EKF
Pˆk−
− xˆk+1
xˆk−
ˆx+ k ˆ+ P k
•
Update
+ xˆk−1
t
Dynamic state estimation
Conclusions
3. Update −1 − T T T Kk = P− k H k H k P k H k + Mk R k Mk ˆ x− x+ x− k =ˆ k + Kk zk − h ˆ k
H=
− T T T P+ k = (I − Kk Hk ) Pk (I − Kk Hk ) + Kk Mk Rk Mk Kk
:
⊗
xˆk+
Pˆk+
58
dh dTS
0
0
0
ˆ x
dh (TS ) M= dv
ˆ x
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
1. DLR Methods
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
5. Conclusions
OHL under test - BR1 Landsnet Weather interpolation using Biharmonic splines at 2016-04-18 21:00 DLR State Estimation
7
2 6.5
David L. Alvarez A.
1 6
64.5° N
64.5° N 0
Introduction
5.5
-1
5
Objective
4.5
-2
State Estimation
4
-3 3.5
Assessment of Algorithms
-4 3
-5 2.5
29
Steady State
-6 2
Dynamic State 21.5° W
Conclusions
:
58
Towers
Conductor
Fx [kN]
Tref [◦ C]
Capacity [MVA]
1-4 4-13 13-23 23-38 38-62 62-72 72-83 83-94 94-95 95-98 98-103 103-104 104-105 105-106 106-109
470-AL3
24.2 28.1 21.2 22.2 25.7 23.1 21.4 33.9 35.1 7.4 6.6 23.8 23.7 36.1 15.2
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
304
109-112
6469AL3134ST4A
49.9
20
112-116 116-120 120-125 125-127 127-129 129-130 130-139 139-143 143-147 147-151 151-155 155-161 161-166 166-172
470-AL3
14.0 21.7 21.6 16.9 10.6 9.4 19.2 17.3 73.6 25.4 39.4 39.7 25.7 47.4
20 20 20 20 20 20 20 20 20 20 20 20 20 20
470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3
470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 470-AL3 774-AL3 2X774-AL3 2X774-AL3 2X774-AL3 2X774-AL3 2X774-AL3
Span
21.5° W
1
2
3
4
5
6
7
8
9
10
289 230 436 421 318 379 388 387 426 197 208 400 392 480 272
387 395 398 343 449 453 389 389
440 302 457 394 386 317 446 294
308 340 408 414 299 429 224
392 277 308 386 411 433 241
410 188 397 441 328 293 455
337 432 414 413 450 377 272
336 268 313 402 418 446 398
359 187 376 441 416 372 414
331 435 410 308 446 366
213 140
194 136
183
162
136
142
146
133
304
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
295
192
304
16
202
909
159
304
17 18 19 20 21 22 23 24 25 26 27 28 29 30
318 316 258 377 270 312 380 373 468 222 441 193 173 368
278 316 383 182 284
371 233 327
329 217 374
255
290 329 329 349 249 398 260 384
362 365 289 337 288 307 276 398
378 347 580 387 349 238 213 385
388
349
303
280
341
351 297 337
316
304 304 304 304 304 304 304 304 304 304 304 304 304
352 304 304 304 304 304 304 304 415 830 830 830 830
Section
340
11
12
13
14
15
16
17
18
19
20
21
22
23
24
435 416
436 433
405 405
208 431
394 395
444
408
428
391
367
353
342
349
375
225 398
354
252
State Estimator Performance - Simulation OHL BR-1 located in Iceland and operated by LandsNet DLR State Estimation
~ S, |ikm | Ta , ϑ,
David L. Alvarez A.
Thermal phenomenon
TS
Mechanical phenomenon
ℓ, D, H
Electro-magnetic phenomenon
R, L, C
Introduction Objective State Estimation Assessment of Algorithms 30
Steady State Dynamic State
Conclusions
Matlab simulations ik
vk
R(Ts , ℓ)
C (D, ℓ)
L(ℓ)
C (D, ℓ)
im
vk , i k , vm , i m vm
Solar Radiation - S
Current - |ikm |
Power Flow R SIMULINK
:
58
R, L, C
Heat Transfer R Matlab
~ Wind - ϑ
State Estimator Performance - Simulation OHL BR-1 Simulation at 18:00 18.04.2016 DLR State Estimation
Weather station report
David L. Alvarez A. Direct and indirect meas. accuracy
Introduction Objective
NWP
State Estimation Assessment of Algorithms
Down scaling 31
Steady State Dynamic State
Direct measurements
Conclusions
Name Ta ϑ δ Ta ϑ δ TS D H v i
Accuracy 2 35 11.25 1 20 11.25 0.5 2.5 0.03 0.3 0.3
Units [K] [%] [◦ ] [K] [%] [◦ ] [K] [cm] [%] [%] [%]
Name
Ta [◦ C]
ϑ [m/s]
Rvk Holms Korpa Geldn Kjaln Skrau Blikd Sfell
3.0 2.1 2.7 3.1 2.0 2.1 1.8 -4.7
3 4 3 3 5 7 5 4
Algorithm 1 1: 2: 3: 5: 6: 7:
Direct Measurements
8: 9:
zTheor.
zmeasured zTheor. + e −125.60 + j26.63 −517.26 + j486.07 −111.39 + j37.95 511.86 − j505.74 16.7 25.353 15.696 10.39
Ruling Span 17 1 15 11
Span Units
10:
1 1 1 1
12:
11:
[kV] [A] [kV] [A] [◦ C] [kN] [kN] [m]
13: 14: 15: 16: 17: 18: 19: 20: 21: 22:
:
58
Name
Ta [◦ C]
ϑ [m/s]
Moshe Tingv Akrfj Tyril Botns Skahe Hamel Hveyr
-0.5 2.5 1.7 2.0 -3.5 -3.5 1.3 1.5
4 3 6 3 5 7 4 5
Wind Direction [◦ ] -68 270 202 135 270 225 225 225
Algorithm
4:
vk −125.78 + j26.667 ik −518.32 + j486.70 vm −111.32 + j37.853 im 513.00 − j506.26 TS17 16.8 H1 25.356 H15 15.698 D11 10.38
Wind Direction [◦ ] 225 225 202 202 247 202 247 -68
23:
Proposed algorithm for DLR state estimation using WLS
procedure DlrSE(z, OHL, ˆ x0 ) ˆx ← ˆx0 ǫ ← 0.01 e←∞ while e ≥ ǫ do if ∃ ˆx.TS ≤ −273 then return error break else h (z, ˆx) ← h(z, ˆ x, OHL) ⊲ Measurement functions T ⊲ Weights matrix W ← diag 1/σ1 2 1/σ2 2 . . . 1/σi 2 H ← ∂h(z, x)/∂x ⊲ Jocabian matrix h i−1 T T ∆ˆx ← [H] [W] [H] [H] [W] [h(z, ˆ x)] ˆx ← ˆx − ∆ˆx e ← max |∆ˆx| if ∃ Im (∆ˆx) 6= 0 then return error break end if end if end while return ˆx end procedure
TS Estimated by Proposed Algorithm
b S = 40 [◦ C] Rb0 = 3.83 [Ω], XbL0 = 25.2 [Ω], YbC0 = 164 [µS], T 0
DLR State Estimation
25
David L. Alvarez A. Introduction
20
Objective State Estimation
15
Assessment of Algorithms 32
Steady State Dynamic State
10
Conclusions
5
0
-5 5 :
58
10
15
Ruling Span
20
25
30
The algorithm converged in 4 iterations
Standard laptop, 8 GB of RAM and Intel R Core i5-1.70 GHz DLR State Estimation
107
David L. Alvarez A. Introduction
106
Objective State Estimation
105
Assessment of Algorithms 33
Steady State Dynamic State
104
Conclusions
103
102
101 :
58
1
1.5
2
2.5
3
3.5
4
Impact of Meas. errors - 1000 runs Average time of 2.6 [s] with 3 or 4 iterations. The maximum distance between whiskers was ≈ 8 [K] DLR State Estimation David L. Alvarez A.
25
Introduction Objective
20
State Estimation Assessment of Algorithms
15 34
Steady State Dynamic State
Conclusions
10
5
0
-5 2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Ruling Span :
58
Comparison between TS estimated and computed using the two weather models DLR State Estimation
8
David L. Alvarez A. Introduction
7
Objective
6
State Estimation Assessment of Algorithms
5 35
Steady State Dynamic State
4
Conclusions
3 2 1 0 2
:
58
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Influence of Direct Measurements DLR State Estimation
5
David L. Alvarez A.
4.5
Introduction Objective
4
State Estimation
3.5
Assessment of Algorithms 36
Steady State
3
Dynamic State
2.5
Conclusions
2 1.5 1 0.5 0 2
:
58
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Dynamic State Estimator Performance Temperature tracking calculation Example - Cigre 601 DLR State Estimation David L. Alvarez A. Introduction Objective
Time [min]
Ta [◦ C]
ϑ [m/s]
δ [◦ ]
t≤0 0 < t ≤ 10 t > 10
24.0 23.7 23.5
1.9 1.7 0.8
55 62 37
S W/m2
Assessment of Algorithms Steady State 37
Conclusions
Type A d ms ma E ′ R25 ◦C βs βa αs ε α cs 20 ◦ C ca 20 ◦ C
Drake 26/7
unit
ACSR 486.6 × 10−6 10.4 × 10−3 0.5119 1.116 57000 × 106 0.0727 × 10−3 1 × 10−4 3.8 × 10−4 0.8 0.8 23 × 10−6 481 897
m2 m kg/m kg/m N/m2 Ω/m 1/K 1/K 1 1 1/K J/K kg J/K kg
Rs Tref Href
Units
300 20 24.2
m ◦C kN
2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12:
ˆx− x+ k ←ˆ k−1 + P− k ← Pk−1 for j ← ∆t to tk step ∆t do ˆx˙ − x− k ←f ˆ k , u, 0, ∆t ˆx− ← ˆx− + ˆx˙ − k
⊲ Predict
k
k
F ← ∂f/∂x|ˆx− ,uk k L ← ∂f/∂w|ˆx− ,uk k ˙ − ← FP− + P− FT + LQLT P k k k − − ˙− Pk ← Pk + P k end for
13: 14: 15: 16: 17: 18: 20:
58
Values
Algorithm 2 Proposed algorithm for DLR State estimation using an EKF + 1: procedure HybridEKF(zk ,uk ,ˆ x+ k−1 ,Pk−1 ,∆t,tk ,Q,Rk )
19:
:
802 819 856
Conductor and span characteristics
State Estimation
Dynamic State
|ikm | [A]
0 0 0
21:
Hk ← ∂h/∂x|ˆx− k Mk ← ∂h/∂v|ˆx−
k −1 − T T Kk ← P− Mk Rk MT k k Hk Hk Pk Hk + x− ⊲ Update xˆ+ x− k k ←ˆ k + Kk zk − h ˆ T + − T Pk ← (I − Kk Hk ) Pk (I − Kk Hk ) + Kk Mk Rk MT k Kk
+ return ˆx+ k , Pk end procedure
Thermal Monitoring - Transient State lower limit |ϑk | = |ϑk |Theor. + 0.5 [m/s] RMSe = 4.02 [K], upper limit |ϑk | = |ϑk |Theor. − 0.5 [m/s], RMSe = 6.73 [K]. DLR State Estimation
70
David L. Alvarez A. Introduction
65
Objective State Estimation
60
Assessment of Algorithms Steady State 38
Dynamic State
55
Conclusions
50
45
40 00:00 :
58
00:10
00:20
00:30
Time
00:40
00:50
Temperature Measurements Estimated wind speed DLR State Estimation
2.5
David L. Alvarez A. Introduction
2
Objective State Estimation Assessment of Algorithms
1.5
Steady State 39
Dynamic State
Conclusions
1
0.5
0 00:00
00:10
00:20
00:30
Time :
58
00:40
00:50
Estimated Temperature
✯, t0 , R = (1.5/3)2 K2 , Update rate = z = TS , x˙ = f x, u, w 60 [s] DLR State Estimation
7
David L. Alvarez A.
6
Introduction
55
Objective
5 State Estimation
50
Assessment of Algorithms
4
Steady State 40
Dynamic State
45
Conclusions
3
2 40 1 35 0 00:00
00:10
00:20
00:30
00:40
00:50
Time
:
RMSe lower limit 0.34 [K] 58
RMSe upper limit 0.54 [K]
RMSe Simulated 0.6 [K]
Predicted Temperature
✯, t0 , R = (1.5/3)2 K2 , Update rate = z = TS , x˙ = f x, u, w 60 [s], ∆tC = 15 [min] DLR State Estimation
15
David L. Alvarez A.
55
Introduction Objective State Estimation
50
10
Assessment of Algorithms Steady State 41
Dynamic State
45
Conclusions
5 40
35 0 00:00
00:10
00:20
00:30
00:40
00:50
Time
RMSe lower limit 1.6 [K] :
58
RMSe upper limit 2.2 [K]
Mechanical Monitoring Tension 0
✯, t , R = (100/3)2 N2 , Update rate = z = H, x˙ = f x, u, w 60 [s] DLR State Estimation
58
21.8
David L. Alvarez A.
56
21.6
54
21.4
State Estimation
52
21.2
Assessment of Algorithms
50
21
48
20.8
46
20.6
44
20.4
42
20.2
Introduction Objective
Steady State 42
Dynamic State
Conclusions
40 00:00
20 00:10
00:20
00:30
00:40
00:50
Time
:
58
RMSe lower limit - estimated 0.18 [K]
RMSe upper limit - estimated 1.5 [K]
RMSe lower limit - predicted 0.22 [K]
RMSe upper limit - predicted 2 [K]
Sag Monitoring z = D, x˙ = f 60 [s] DLR State Estimation
58
David L. Alvarez A.
56
✯, t0 , R = (0.2/3)2 m2 , Update rate = x, u, w 9.1 9
Introduction
54
Objective
8.9
State Estimation
52
Assessment of Algorithms
50
8.7
48
8.6
8.8
Steady State 43
Dynamic State
Conclusions
8.5
46
8.4 44 8.3 42 40 00:00
8.2 8.1 00:10
00:20
00:30
00:40
00:50
Time
:
58
RMSe lower limit - estimated 0.28 [K]
RMSe upper limit - estimated 1.5 [K]
RMSe lower limit - predicted 0.29 [K]
RMSe upper limit - predicted 1.5 [K]
Performance Comparison 1000 simulations for each one of direct measurements DLR State Estimation David L. Alvarez A. Introduction Objective
Performance comparison between the three kind of direct measurements for 1000 random cases
State Estimation Assessment of Algorithms Steady State 44
Dynamic State
Conclusions
:
58
Measurement
Avg. RMSe [K]
Avg. Time [s]
Temperature Tension Sag
0.303 0.253 0.328
0.0593 0.0598 0.0602
Dynamic Estimation Algorithm Validation Testing scheme DLR State Estimation
W1
W2
Transformer
z1
z2
z1′
z2′ y2′ x2′
David L. Alvarez A.
A V1
V2
y1
y2
y1′
U1
U2
x1
x2
x1′
Introduction
OHL conductor
ikm
−
+
Objective
V State Estimation Assessment of Algorithms Steady State 45
Dynamic State
Type Standart A d ms ma ′ R50 ◦ C,60 Hz βs βa αs εs α cs 20 ◦ C ca 20 ◦ C
Conclusions
:
58
Linnet ACSR 26/7 ASTM B 232 198.38 × 10−6 18.31 × 10−3 0.217 0.472 0.2095 × 10−3 1 × 10−4 3.8 × 10−4 0.5 0.5 23 × 10−6 481 897
unit
m2 m kg/m kg/m Ω/m 1/K 1/K 1 1 1/K J/K kg J/K kg
Test Setup EM&D- Laboratory, UNAL - Bogota, Colombia DLR State Estimation David L. Alvarez A. Introduction Objective State Estimation Assessment of Algorithms Steady State 46
Dynamic State
Conclusions
:
58
Assumed Conditions - Planned case 1: assumed conditions ǫs = 0.5, case 2: |ϑk | = |ϑk |fore. − 0.5 [m/s] ǫs = 0.2, case 3: |ϑk | = |ϑk |fore. + 0.5 [m/s], ǫs = 0.9 DLR State Estimation
2.5 450
David L. Alvarez A. Introduction
400
2
Objective State Estimation
350
Assessment of Algorithms
1.5
300
Steady State 47
Dynamic State
250
Conclusions
1 200 150 0.5 100 0
50 12:00
13:00
14:00
Time :
58
15:00
16:00
Measurements
z = TS , x˙ = f (x, u, w , t), Q = (5/3)2 A2 , (1.5/3)2 K2 , R = (1.5/3)2 K2 , Update rate = 30 [s]
DLR State Estimation
450
David L. Alvarez A.
60
Introduction
400
Objective
50
State Estimation Assessment of Algorithms
350 300
40
Steady State 48
Dynamic State
Conclusions
250
30
200 20 150 10
100 50
0 12:00
13:00
14:00
Time :
58
15:00
16:00
Uncertainty Influence case 1: RMSǫ = 2.4 [K], case 2: RMSǫ = 5.7 [K], case 3: RMSǫ = 5.5 [K] DLR State Estimation
70
David L. Alvarez A.
65
Introduction
60
Objective State Estimation
55
Assessment of Algorithms
50
Steady State 49
Dynamic State
45
Conclusions
40 35 30 25 20 12:00 :
58
13:00
14:00
Time
15:00
16:00
Estimated Parameters DLR State Estimation
3
0.9
David L. Alvarez A.
0.8
Introduction
2.5
Objective
0.7
State Estimation
2
Assessment of Algorithms
0.6
Steady State 50
Dynamic State
1.5
0.5
Conclusions
0.4 1 0.3 0.5 0.2 0
0.1 12:00
13:00
14:00
Time :
58
15:00
16:00
EKF - Estimated Temperature Using case 2: RMSǫ = 1.5 [K] DLR State Estimation David L. Alvarez A.
60
Introduction
25
Objective State Estimation
50
20
40
15
30
10
20
5
Assessment of Algorithms Steady State 51
Dynamic State
Conclusions
10
0 12:00
13:00
14:00
Time :
58
15:00
16:00
EKF - Predicted Temperature Using case 2: RMSǫ = 2.5 [K] DLR State Estimation David L. Alvarez A.
60
Introduction
25
Objective State Estimation
50
20
40
15
30
10
20
5
Assessment of Algorithms Steady State 52
Dynamic State
Conclusions
10
0 12:00
13:00
14:00
Time :
58
15:00
16:00
1
Introduction
2
Objective
3
State Estimation
4
Assessment of Algorithms
5
Conclusions
1. DLR Methods
3. Steady state
4. Validation →Simulations
3. Dynamic State
4. Validation →Simulations, test
5. Conclusions
Conclusions Concluding Remarks DLR State Estimation
1. A state estimation methodology was proposed both steady and dynamic state
David L. Alvarez A. Introduction
OHL ratings
Network data
Objective
◮ Conductor data ◮ OHL geometry ◮ Configuration
State Estimation
State prediction
State estimation
◮ GIS data
DLR
Assessment of Algorithms Conclusions
Downscaling Weather Nowcast
53
Numerical Weather Prediction - NWP
Indirect Methods
PMU vk , i k , vm , i m
Sag Tension Temperature
Direct Methods
2. This methodology runs with typical DLR measurements Technology DGPS PLS Power DonutTM
58
Communication Measurements TCP-IP ZigBee GSM, GPRS, EDGE, ZigBee DNP, Modbus, GSM, CDMA GSM, GPRS, DNP3, IEC61850 GSM IEEE C37.118
R Sagometer
Sag
Ampacimon
Sag
CAT-1
Tension Sag - Temperature
PMU :
Parameter Sag Temperature Sag - Temperature
D TS i , V , T , θ, P, Q Image f
Tension, H v, i
Conclusions Concluding Remarks DLR State Estimation
3. Expressions to implement the proposed SE algorithms were derived
David L. Alvarez A.
Introduction Objective State Estimation Assessment of Algorithms Conclusions
54
∂ Re (hv (z, x)) ∂R ∂ Im (hv (z, x)) ∂R ∂ Re (hi (z, x)) ∂R ∂ Im (hi (z, x)) ∂R ∂hR (z, x) ∂R H= ∂hE (z, x) ∂R 0 0 0 0
∂ Re (hv (z, x)) ∂YC ∂ Im (hv (z, x)) ∂YC ∂ Re (hi (z, x)) ∂YC ∂ Im (hi (z, x)) ∂YC
∂ Re (hv (z, x)) ∂XL ∂ Im (hv (z, x)) ∂XL ∂ Re (hi (z, x)) ∂XL ∂ Im (hi (z, x)) ∂XL 0
0 ∂hE (z, x) ∂YC ∂hP (z, x) ∂YC
0 0 0
0
0
0
0
0
0
0 0 ∂hR (z, x) ∂TS ∂hE (z, x) ∂TS ∂hP (z, x) ∂TS ∂hTS (z, x) ∂TS ∂hH (z, x) ∂TS ∂hD (z, x) 0
∂TS
4. This research proposed the integration of direct and indirect DLR measurements Electro-Magnetic i, v E~
TS , P, σ R, L, C Thermal ~ Q, Ta , S, ϑ
:
58
D, ℓ
Mechanical H
Conclusions Concluding Remarks DLR State Estimation David L. Alvarez A. Introduction
5. To simulate and test the algorithms, these showed computational efficiency and stability
Objective State Estimation Assessment of Algorithms Conclusions
107
2.5
106
2
55 105
1.5 104
1 103
0.5 102
101
1
1.5
2
2.5
3
3.5
4
0 00:00
00:10
00:20
00:30
Time
:
58
00:40
00:50
Conclusions Published researches DLR State Estimation
◮ David L Alvarez, Filipe Faria Miguel da Silva, Claus Leth Bak,
David L. Alvarez A.
Enrique E Mombello, and Javier A Rosero. Dynamic line rating Technologies and challenges of PMU on overhead lines: A survey. In 2016 51st International Universities Power Engineering Conference (UPEC), pages 1–6, Coimbra, sep 2016. IEEE Press ◮ David Alvarez, Filipe Miguel Faria da Silva, Claus Leth Bak, Enrique
Introduction Objective State Estimation Assessment of Algorithms Conclusions
56
Mombello, Javier Rosero, and Daniel Olason. A Methodology to Assess PMU in the Estimation of Dynamic Line Rating. Generation, Transmission Distribution, IET- Under Review - Round 1, 2017 ◮ David L Alvarez, F Faria, Enrique E Mombello, Claus Leth, and Javier A Rosero. An Approach to Dynamic Line Rating State Estimation at Thermal Steady State Using Direct and Indirect Measurements. Electric Power Systems Research - Accepted, 2017 ◮ David Alvarez, Filipe Miguel Faria da Silva, Enrique E Mombello, Claus Leth Bak, and Javier A Rosero. Dynamic Line Rating Estimation and Prediction at Thermal Transient State. IEEE Transactions on Power Delivery - Under Review, 2017
:
58
Conclusions Future Works DLR State Estimation David L. Alvarez A. Introduction Objective
1. Several assumptions were considered in the assessment of the algorithms
State Estimation Assessment of Algorithms Conclusions
57
2. The algorithms were based on available true measurements 3. Field measurements on a real OHLs under typical operating conditions need to be considered 4. A framework can be developed
:
58
Assessment with Field Measurements 2 2 2 2
z = TS , D, RTS = (1.5/3) K , RD = (0.1/3) m , Qikm = (5/3)2 A2 , QTa = (1.5/3)2 K2 , Update rate = 5 [min]
DLR State Estimation
40
David L. Alvarez A.
30
35 25 30
Introduction Objective
Rs Tref Href
State Estimation Assessment of Algorithms Conclusions
Values 82.3 20 4.130
Units m ◦C kN
20
25 20
15 15 10
10 5
5
0
58
0 06:00
09:00
12:00
15:00
18:00
21:00
Time - [h:m] 40
40
2.7
35
2.6
30
2.5
25
2.4
10
20
2.3
5
15
2.2
0
10 06:00
30
35 25 30 20
25 20
15 15 10 5 0 06:00
09:00
12:00
15:00
Time - [h:m]
:
58
18:00
21:00
2.1 09:00
12:00
15:00
Time - [h:m]
18:00
21:00
Thank you for your attention Questions?
David L. Alvarez Phone +57 301 4413314 Email:
[email protected] Web: www.ing.unal.edu.co/grupos/emd/
