Post on 15-Mar-2018
Advanced Monitoring and Data Analytics in Power Distribution Systems
Hamed Mohsenian-Rad
Associate Professor, Electrical Engineering, University of California, RiversideAssociate Director, Winston Chung Global Energy Center
Director, UC-National Lab Center for Power Distribution Cyber SecurityDirector, Smart Grid Research Lab
Talk at UCR Solar Conference, 3/1/2018
Acknowledgements: A. Shahsavari, M. Farajollahi, Z. Taylor, E. Stewart, E. Cortez, A. Van-Meier, L. Alvarez, C. Roberts, F. Megala, S. Ula, H. Akhavan-Hejazi, A. Martinez-Morales, M. Barth
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 1 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room Palo Verde Nuclear Power Plant
230 kV Substation
City of Riverside (Population: 300,000)
Substation
……
Grid Edge
69 kV / 12 kV
≥ 230 kV
Transmission
Distribution
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 2 / 26
Power Distribution and Distributed Energy Resources
HunterSubstation
Circuit #1224 (12 kV)
1 MWh / 200 kW
460 kW
460 kW
UCR CE-CERT/ WCGEC
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 3 / 26
Power Distribution and Distributed Energy Resources
HunterSubstation
Circuit #1224 (12 kV)
1 MWh / 200 kW
460 kW
460 kW
UCR CE-CERT/ WCGECData Stream (1 min)
SCADA
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 4 / 26
Load Profile of Distribution Feeders
SCADA: Circuit #1224 (12 kV)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 5 / 26
DER Signatures
Coordinated Measurements: Circuit #1224 (12 kV)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 6 / 26
DER Optimization
Stochastic Online Optimization: Feeder Peak Load Shaving
97 kW
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 7 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room Palo Verde Nuclear Power Plant
230 kV Substation
City of Riverside (Population: 300,000)
Substation
……
Grid Edge
69 kV / 12 kV
≥ 230 kV
Transmission
Distribution
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 7 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room
Transmission Lines
Substations
Palo Verde Nuclear Power Plant
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
≥ 230 kV
Transmission
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 8 / 26
Measuring Phasors
PMU Sensor
FFT ↦ Fundamental Component
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 8 / 26
Measuring Phasors
PMU Sensor
FFT ↦ Fundamental Component
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
TimeReference
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 8 / 26
Measuring Phasors
PMU Sensor
FFT ↦ Fundamental Component
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
TimeReference
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 8 / 26
Measuring Phasors
PMU Sensor
FFT ↦ Fundamental Component
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
TimeReference
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 8 / 26
Measuring Phasors
PMU Sensor
FFT ↦ Fundamental Component
𝑣 𝑡 = 𝑉 cos(𝜔𝑡 + ∠𝑉)
𝑉 ∠𝑉
Phasor Representation
TimeReference
GPS Satellites
Synchro
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 9 / 26
Application of Synchrophasors
30 fps
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 9 / 26
Application of Synchrophasors
𝑃12 ∝ Ð𝑉1 −Ð𝑉2
30 fps
RPAD
200 Miles
Bus 1
Ð𝑉1
𝑉1 Ð𝑉1
Bus 212P
𝑉2 Ð𝑉2Ð𝑉2
0.59 Hz0.64 HzInter-area Oscillations
Stability Analysis
Model Validation
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 10 / 26
Application of Synchrophasors
𝑑𝑓
𝑑𝑡∝ 𝑃Supply−𝑃Demand
GPS-SynchronizedFrequency Measurements
Power Plant Location
Sensor Location
Loss of Power PlantWesternInterconnection
GPS-SynchronizedFrequency Measurements
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 11 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room Palo Verde Nuclear Power Plant
230 kV Substation
City of Riverside (Population: 300,000)
Substation
……
Grid Edge
69 kV / 12 kV
≥ 230 kV
Transmission
Distribution
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 11 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room Palo Verde Nuclear Power Plant
230 kV Substation
City of Riverside (Population: 300,000)
Substation
……
Grid Edge
69 kV / 12 kV
≥ 230 kV
Transmission
Distribution
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 11 / 26
Power Grid
WesternInterconnection
Grand Coulee Dam
CAISO Control Room Palo Verde Nuclear Power Plant
230 kV Substation
City of Riverside (Population: 300,000)
Substation
……
Grid Edge
69 kV / 12 kV
≥ 230 kV
Transmission
Distribution
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 12 / 26
Distribution Synchrophasors
• New Technology
• Augmented PMUs or Power Quality Sensors
• Features
• Reporting Rate: 120 fps
• Three-Phase
• Both Voltage and Current
• Deployment
• Few pilot projects, including in Riverside, CA
• Advantages and Applications
• Yet to be Explored
D-PMUs /
Micro-PMUs (PSL)
100,000 More Data Points than Smart Meter
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 13 / 26
Distribution Synchrophasors
Medium Voltage Low Voltage
Circuit 6
...
...
Substation: 69 kV / 12 kV
OLTC Fuse
Cap Bank
CircuitBreaker
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 13 / 26
Distribution Synchrophasors
Circuit 6
...
...
Substation: 69 kV / 12 kV
OLTC Fuse
Cap Bank
CircuitBreaker
Medium Voltage Low Voltage
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 13 / 26
Distribution Synchrophasors
Circuit 6
...
...
Substation: 69 kV / 12 kV
OLTC Fuse
Cap Bank
CircuitBreaker
Medium Voltage Low Voltage
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 13 / 26
Distribution Synchrophasors
Circuit 6
...
...
Substation: 69 kV / 12 kV
OLTC Fuse
Cap Bank
CircuitBreaker
Medium Voltage Low Voltage
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 14 / 26
Event/Signature Analysis
Sensor
Phase A
120 fps
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 14 / 26
Event/Signature Analysis
Sensor
Phase A
120 fps
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 14 / 26
Event/Signature Analysis
Sensor
120 fps
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 14 / 26
Event/Signature Analysis
Sensor
120 fps
Question: Is this event worth studying?
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 15 / 26
Problem Statement
Distribution Substation
OtherFeeders
…
1 2
3-5
8-1
2
6 7 13
14-19
20 28 29 30
21
-27
𝐼𝑢 ∠𝐼𝑢𝑉𝑢 ∠𝑉𝑢,
Questions:
1. What is the source location of this event?
2. What can we learn from this event?
𝐼𝑑 ∠𝐼𝑑𝑉𝑑 ∠𝑉𝑑 ,
Upstream Downstream
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 16 / 26
Background: Compensation Theory
_+ V
_+
Vpre
Ipre Z
pre
_+ V
post
Ipost Z
post
Vposts V
postr
Ipostsr
Vpre
s Vpre
rI
presr
Vs Vr Isr
I
Pre-Event
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 16 / 26
Background: Compensation Theory
_+ V
_+
Vpre
Ipre Z
pre
_+ V
post
Ipost Z
post
Vposts V
postr
Ipostsr
Vpre
s Vpre
rI
presr
Vs Vr Isr
I
Pre-Event
Event
Post-Event
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 16 / 26
Background: Compensation Theory
_+ V
_+
Vpre
Ipre Z
pre
_+ V
post
Ipost Z
post
Vposts V
postr
Ipostsr
Vpre
s Vpre
rI
presr
Vs Vr Isr
I
Pre-Event
Event
Post-Event
V_
+
Vr Isr
I
Equivalent Circuit
∆𝑉 = 𝑉𝑝𝑜𝑠𝑡 − 𝑉𝑝𝑟𝑒
∆𝐼 = 𝐼𝑝𝑜𝑠𝑡 − 𝐼𝑝𝑟𝑒
Sou
rces
Rem
ove
d
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 17 / 26
Step 1: Extract Differential Synchrophasors
Upstream Sensor Downstream Sensor
𝐼𝑢∠𝐼𝑢
𝑉𝑢
∠𝑉𝑢
𝐼𝑑∠𝐼𝑑
𝑉𝑑
∠𝑉𝑑
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 17 / 26
Step 1: Extract Differential Synchrophasors
Upstream Sensor Downstream Sensor
𝐼𝑢∠𝐼𝑢
𝑉𝑢
∠𝑉𝑢
𝐼𝑑∠𝐼𝑑
𝑉𝑑
∠𝑉𝑑
∆𝐼𝑢 ∠∆𝐼𝑢
Pre
-Eve
nt
Post
-Eve
nt
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 17 / 26
Step 1: Extract Differential Synchrophasors
Upstream Sensor Downstream Sensor
𝐼𝑢∠𝐼𝑢
𝑉𝑢
∠𝑉𝑢
𝐼𝑑∠𝐼𝑑
𝑉𝑑
∠𝑉𝑑
∆𝐼𝑢 ∠∆𝐼𝑢
Pre
-Eve
nt
Post
-Eve
nt
∆𝑉𝑢 ∠∆𝑉𝑢
Pre
-Eve
nt
Post
-Eve
nt
∆𝐼𝑑 ∠∆𝐼𝑑P
re-E
ven
t
Post
-Eve
nt
∆𝑉𝑑 ∠∆𝑉𝑑
Pre
-Eve
nt
Post
-Eve
nt
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown)Forward
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward 𝑘: Event Bus (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward 𝑘: Event Bus (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Pseudo-Measurements
Forward 𝑘: Event Bus (Unknown)
(Feeder Data, Transformer Ratings)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward 𝑘: Event Bus (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward
∆𝑉𝑘+1𝑓
= ∆𝑉𝑘𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓+ ∆𝐼𝑘 𝑍𝑘
Event Current (Unknown)
𝑘: Event Bus (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward
∆𝑉𝑘+1𝑓
≠ ∆𝑉𝑘𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓+ 𝑌𝑘∆𝑉𝑘
𝑓𝑍𝑘
Incorrect
𝑘: Event Bus (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward
∆𝑉𝑘+1𝑓
≠ ∆𝑉𝑘𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓+ 𝑌𝑘∆𝑉𝑘
𝑓𝑍𝑘
𝑘: Event Bus (Unknown)
∆𝑉𝑛𝑓≠ ∆𝑉𝑛−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑛−1∆𝑉𝑛−1
𝑓𝑍𝑛−1
⋮
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 18 / 26
Step 2: Forward Nodal Voltage Calculation
∆𝑉1𝑓= ∆𝑉𝑢
∆𝑉2𝑓= ∆𝑉1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓𝑍1
⋮
∆𝑉𝑘𝑓= ∆𝑉𝑘−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓𝑍𝑘−1
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
Forward
∆𝑉𝑘+1𝑓
≠ ∆𝑉𝑘𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑘−1∆𝑉𝑘−1
𝑓+ 𝑌𝑘∆𝑉𝑘
𝑓𝑍𝑘
𝑘: Event Bus (Unknown)
I
∆𝑉𝑛𝑓≠ ∆𝑉𝑛−1
𝑓+ ∆𝐼𝑢 + 𝑌1∆𝑉1
𝑓+⋯+ 𝑌𝑛−1∆𝑉𝑛−1
𝑓𝑍𝑛−1
⋮
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
∆𝑉𝑘−1𝑏 = ∆𝑉𝑘
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 + ∆𝐼𝑘 𝑍𝑘−1
Event Current (Unknown)
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
∆𝑉𝑘−1𝑏 ≠ ∆𝑉𝑘
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 + 𝑌𝑘∆𝑉𝑘𝑏 𝑍𝑘−1
Incorrect
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
∆𝑉𝑘−1𝑏 ≠ ∆𝑉𝑘
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 + 𝑌𝑘∆𝑉𝑘𝑏 𝑍𝑘−1
∆𝑉1𝑏 ≠ ∆𝑉2
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌2∆𝑉2
𝑏 𝑍1
⋮
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 19 / 26
Step 3: Backward Nodal Voltage Calculation
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) Backward
II
∆𝑉𝑛−1𝑏 = ∆𝑉𝑛
𝑏 + ∆𝐼𝑑 + 𝑌𝑛∆𝑉𝑛𝑏 𝑍𝑛−1
⋮
∆𝑉𝑛𝑏 = ∆𝑉𝑑
∆𝑉𝑘𝑏 = ∆𝑉𝑘+1
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 𝑍𝑘
∆𝑉𝑘−1𝑏 ≠ ∆𝑉𝑘
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌𝑘+1∆𝑉𝑘+1
𝑏 + 𝑌𝑘∆𝑉𝑘𝑏 𝑍𝑘−1
∆𝑉1𝑏 ≠ ∆𝑉2
𝑏 + ∆𝐼𝑢 + 𝑌𝑛∆𝑉𝑛𝑏 +⋯+ 𝑌2∆𝑉2
𝑏 𝑍1
⋮
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 20 / 26
Step 4: Event Location Identification
Y1
Z1 Zn-1
Ik
Vn Vk
|Vd| V
d
|Id| I
dZ
u Zd
V2 Vn-1 V1
I1
Y2
I2
Yk
Ik
Yn-1
In-1
Yn
In
Downstream
|Vu| V
u
|Iu| I
u
Upstream
Zk-1 Vk-1
Ik-1
Zk Vk+1
Ik+1
𝑘: Event Bus (Unknown) BackwardForward
∆𝑉1𝑓, ⋯ , ∆𝑉𝑘−1
𝑓, ∆𝑉𝑘
𝑓, ∆𝑉𝑘+1
𝑓, ⋯ , ∆𝑉𝑛
𝑓
∆𝑉1𝑏, ⋯ , ∆𝑉𝑘−1
𝑏 , ∆𝑉𝑘𝑏, ∆𝑉𝑘+1
𝑏 , ⋯ , ∆𝑉𝑛𝑏
Correct
Correct
Incorrect
Incorrect
Forward:
Backward:
𝑘 = argmin ∆𝑉𝑖𝑓− ∆𝑉𝑖
𝑏
𝑖
Φ𝑖
Discrepancy
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 21 / 26
Case Study: Computer Simulation
(a) Event at Bus 24; (b) Event at Bus 36; (c) Event at Bus 9
31 2 4 5
22 3031
32
33
34
3536
37 38 39
41
40
42
4344
6 7 8 9
1011
12 13
14
15
1617181920
21
23
24
25
26
27 28 29
Mic
ro-P
MU
1
Micro-PMU 2
Mic
ro-P
MU
4
Micro-PMU 3
Event Location
Event Location
Event Location
Discrepancy
IEEE
12
3-B
us
Test
Sys
tem
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 21 / 26
Case Study: Computer Simulation
(a) Event at Bus 24; (b) Event at Bus 36; (c) Event at Bus 9
31 2 4 5
22 3031
32
33
34
3536
37 38 39
41
40
42
4344
6 7 8 9
1011
12 13
14
15
1617181920
21
23
24
25
26
27 28 29
Mic
ro-P
MU
1
Micro-PMU 2
Mic
ro-P
MU
4
Micro-PMU 3
Event Location
Event Location
Event Location
Discrepancy
IEEE
12
3-B
us
Test
Sys
tem
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 21 / 26
Case Study: Computer Simulation
(a) Event at Bus 24; (b) Event at Bus 36; (c) Event at Bus 9
31 2 4 5
22 3031
32
33
34
3536
37 38 39
41
40
42
4344
6 7 8 9
1011
12 13
14
15
1617181920
21
23
24
25
26
27 28 29
Mic
ro-P
MU
1
Micro-PMU 2
Mic
ro-P
MU
4
Micro-PMU 3
Event Location
Event Location
Event Location
Discrepancy
IEEE
12
3-B
us
Test
Sys
tem
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 21 / 26
Case Study: Computer Simulation
(a) Event at Bus 24; (b) Event at Bus 36; (c) Event at Bus 9
31 2 4 5
22 3031
32
33
34
3536
37 38 39
41
40
42
4344
6 7 8 9
1011
12 13
14
15
1617181920
21
23
24
25
26
27 28 29
Mic
ro-P
MU
1
Micro-PMU 2
Mic
ro-P
MU
4
Micro-PMU 3
Event Location
Event Location
Event Location
Discrepancy
IEEE
12
3-B
us
Test
Sys
tem
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 21 / 26
Case Study: Computer Simulation
(a) Event at Bus 24; (b) Event at Bus 36; (c) Event at Bus 9
31 2 4 5
22 3031
32
33
34
3536
37 38 39
41
40
42
4344
6 7 8 9
1011
12 13
14
15
1617181920
21
23
24
25
26
27 28 29
Mic
ro-P
MU
1
Micro-PMU 2
Mic
ro-P
MU
4
Micro-PMU 3
Event Location
Event Location
Event Location
Discrepancy
IEEE
12
3-B
us
Test
Sys
tem
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 22 / 26
Case Study: Asset Monitoring
Three-Phase Switched Capacitor Bank
Rating: 3 x 300 kVAR = 900 kVAR
Volt/VAR Control
Onsite Switch On / Switch Off Controller
No Monitoring
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 23 / 26
Case Study: Asset Monitoring
Typical Issues:
Unbalanced Operation (Fuses) Switching Operation (Controllers)1 2
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 23 / 26
Case Study: Asset Monitoring
Typical Issues:
Unbalanced Operation (Fuses) Switching Operation (Controllers)1 2
Remote Monitoring?
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 24 / 26
Case Study: Asset Monitoring
Switch Off Event
(Micro-PMU 1)
Location Identification
(Micro-PMU 2)
Event Bus: 25 (Correct)
DiscrepancyData Analytics
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 24 / 26
Case Study: Asset Monitoring
Switch Off Event
(Micro-PMU 1)
Reactive Power Support
Slightly Unbalanced Operation
Phase B is always higher
Likely fuse blowing on C and A
Data Analytics
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 24 / 26
Case Study: Asset Monitoring
Switch Off Event
(Micro-PMU 1)
Switching Transient
Two-Step 3-Phase Switch
Step 1: Phase C (Zero Crossing)
Step 2: Phase A/B (Possible Malfunction)
C
B
A
Data Analytics
Hamed Mohsenian-Rad Monitoring and Data Analytics in Power Distribution UC Riverside 25 / 26
Big Data Analytics
Raw Data Stream
(Terabytes Per Day)
Big Data Analytics
++++++
Asset Monitoring
State Estimation
Statistical Modeling
Dynamic Modeling
Cyber Security
DER Operation
Market Operation
…
Useful Information