56
Comprehensive Dynamic Reactive Power Planning for Transmission Stability Enhancement Ahmad Tahboub [email protected] Dr. Mohamed Elmoursi [email protected]
Comprehensive Dynamic Reactive Power Planning for Transmission
Stability Enhancement
Ahmad Tahboub [email protected]
Dr. Mohamed Elmoursi [email protected]
What Traditional Utilities Are Seeing
• “Never in recent history has
deployment of capital been more
difficult within the energy industry”
• Revenue of dispatchable (traditional)
generation lower in a merit order
market. But dispatchable is what keeps
the lights on
• The growing duck2
Reminds You of Something?
3
Depleted Dynamic VAR Reserves
4Source: Final Report on the August 14, 2003 Blackout in the United States and Canada
And Generators Stressed
5Source: Final Report on the August 14, 2003 Blackout in the United States and Canada
Standard Violations or Standard Inadequacy?
Recommendation 7
• The unsafe conditions can be said to have resulted
from violations of NERC planning criteria
• On the other hand, investigators believe these
deficiencies are also symptomatic of a systematic
breakdown of the reliability studies and practices
that allowed unsafe voltage criteria to be set and
used in study models
• There were also issues identified with reactive
characteristics of loads
NERC Planning Standard III.C (Year 2004)
• S1: All generators operated with excitation in
the automatic voltage control unless
approved by the TSO
• S2: Generators shall maintain a network
voltage or reactive power output as required
by TSO within the reactive capability.
6
Why Dynamic VAR Reserve Diminished
7Source: Voltage Stability of Electric Power Systems. Thierry Van Cutsem, Costas Vournas
New Standard: VAR-002-4 R2 (Year 2016)
• Unless exempted by TSO, each Generator shall maintain the voltage or VAR
schedule (within facility’s capabilities) provided by TSO, or otherwise shall meet
the conditions of notification for deviations from the voltage or VAR schedule
provided by the Transmission Operator.
• Footnote: Generating facility capability may be established by test or other
means, and may not be sufficient at times to pull the system voltage within the
schedule tolerance band. Also, when a generator is operating in manual control,
reactive power capability may change based on stability considerations.
8Source: NERC Reliability Standards Complete Set. Available online.
More Lessons Learned
• NERC found that some reliability coordinators and control area operators had not
received adequate training in recognizing and responding to system emergencies. Most
notable was the lack of realistic simulations.
• The term “realistic simulations” includes a variety of tools and methods that present
operating personnel with situations to improve and test diagnostic skills in an
environment that resembles expected conditions during a particular type of system
emergency.
9Source: Final Report on the August 14, 2003 Blackout in the United States and Canada. Approved Recommendations. Recommendation 6
What Do We Know So Far?
• Investment getting more difficult
• Generation getting more stressed
• Need more realistic simulations
• How do we evaluate dynamic VAR adequacy?
10
What VAR Planning Means
• What are the optimum locations, sizes and types of reactive power
compensation?
• Minimum investment cost, losses, generation cost
• Maximum stability
• Mixed-Integer Nonlinear Programming
11
Static VAR Planning
• V magnitude is a poor indicator • Preserve “Static Stability Margin”
P
V
Compensation
Acceptable
Range1 2
3
Pre Disturbance
Post Disturbance
V
P
• Where is the POC?• Number of contingencies
12
Dynamic VAR Planning
1
2
Corrective
Action
Disturbance
3
3'
eqP
V
P
4
• Static is an OPF problem, it assumes dynamic stability
13
What Have People Done?
14Also, test systems usually not stressed enough and/or without IM or OXL
Example of Sensitivity Analysis
• Faults randomly selected
• Static sensitivity analysis
• STATCOM only
• System not stressed
• Fault only
15
Recent PhD Theses Future Work
20071. Consideration of other stability/security
constraints. This research has focused on the reactive power control planning to increase the voltage stability margin and to mitigate the transient voltage dip. Other stability/security constraints such as transient stability and post-contingency bus voltage magnitude requirements may also be included in the optimization formulation of the reactive power control planning.
2. Economic benefit analysis and cost allocation. The planned reactive power control devices are intended to serve as control response for contingencies. Further research on quantifying the economic benefit of these devices and efficiently allocating the investment cost under is challenging but important.
20151. Comparing the effectiveness of
different types of dynamic VARsupport strategies and their cost/benefit assessment.
2. Utilization of reactive support from geographically distributed, power electronics based distributed generation (DG) resources.
3. Improvisation in the dynamic optimization procedure through parallelization,multistart algorithms.
16
The Rest of This Presentation
1. Multi-Contingency Dynamic VAR Planning
2. Multiple-Type Multi-Contingency Dynamic VAR Planning
3. Dynamic VAR Planning for Rotor Angle Stability Improvement
4. Final Remarks
17
Complete Objective Function
18
minimize
𝛾1
𝑏=1
𝐵
𝜓𝑏𝐶𝑏 𝑗𝑏 + 𝛾2
𝑓=1
𝐹
max𝐵𝑓,𝜙
𝑡𝑐,𝑓
𝑇𝑏,𝑓 𝜙𝑣𝑟𝑒𝑓 − 𝑣𝑏,𝑓 𝑡 − 𝑡𝑐 , 𝜙
𝐹 𝑇𝑏,𝑓 𝜙 − 𝑡𝑐,𝑓
+𝛾3
𝑘=1
𝐾
𝑏=1
𝐵
𝑡𝑘
𝑇𝛽|𝑣𝑏,𝑟𝑒𝑓 − 𝑣𝑏,𝑘 𝑡 − 𝑡𝑘 , 𝜙 |
𝐵𝐾 𝑇𝛽 − 𝑡𝑘+ 𝛾4
𝑏=1
𝐵
𝑡𝑑𝑖𝑠𝑡
𝑇𝛾|𝑣𝑏,𝑟𝑒𝑓 − 𝑣𝑏 𝑡 − 𝑡𝑑𝑖𝑠𝑡, 𝜙 |
𝐵 𝑇𝛾 − 𝑡𝑑𝑖𝑠𝑡
Max or Mean?
19
𝑓2 =
𝑓=1
𝐹
max𝐵𝑓,𝜙
𝑡𝑐,𝑓
𝑇𝑏,𝑓 𝜙𝑣𝑟𝑒𝑓 − 𝑣𝑏,𝑓 𝑡 − 𝑡𝑐 , 𝜙
𝐹 𝑇𝑏,𝑓 𝜙 − 𝑡𝑐,𝑓
ct
v ( . .)p u
t ( )sct
v ( . .)p u
t ( )s
Constraints (1/2)
20
𝑃𝐺 − 𝑃𝐿 − 𝑃 𝑉, 𝜃 = 0
𝑄𝐺 − 𝑄𝐿 − 𝑄 𝑉, 𝜃 = 0
𝑃𝐺min ≤ 𝑃𝐺 ≤ 𝑃𝐺
max
𝑄𝐺min ≤ 𝑄𝐺 ≤ 𝑄𝐺
max
𝑉min ≤ 𝑉 ≤ 𝑉max
𝑆𝑙 𝑉, 𝜃 ≤ 𝑆𝑙𝑚𝑎𝑥
𝑀𝑉𝐴𝑅𝑏min ≤ 𝑀𝑉𝐴𝑅𝑏 ≤ 𝑀𝑉𝐴𝑅𝑏
max
𝑓𝑖𝑛𝑖𝑡 𝑥0, 𝑦0 = 0
𝑥 = 𝑓 𝑥, 𝑦, 𝑢, 𝜙
0 = 𝑔 𝑥, 𝑦, 𝑢, 𝜙
max𝑑 𝛥𝛿𝑖𝑗 𝑡 ≤ 𝜎
Constraints (2/2)
21
𝑇𝑏,𝑓• 𝜙 − 𝑡𝑐 ≤ 𝑇max
min𝐵 𝑣𝑏,𝑓 𝑇𝐿𝑆 − 𝑡𝑐 , 𝜙 ≥ 𝑣𝑠𝑠,𝑚𝑖𝑛
min 𝑣𝑏,𝑘 𝑡 − 𝑡𝑘 , 𝜙 ≥ 𝑎𝑝𝑒𝑎𝑘 × 𝑣𝑏,𝑘 𝑡𝑘−, 𝜙
𝑇𝑏,𝑘 𝜙 ≤𝑎𝑐𝑦𝑐𝑙𝑒𝑠
𝑓𝑒
min𝐵 𝑣𝑏,𝑘 𝑇𝐿𝑆 − 𝑡𝑘 , 𝜙 ≥ 𝑣𝑠𝑠,𝑚𝑖𝑛
min𝐵 𝑣𝑏,𝑑𝑖𝑠𝑡 𝑇𝐿𝑆 − 𝑡𝑑𝑖𝑠𝑡, 𝜙 ≥ 𝑣𝑠𝑠,𝑚𝑖𝑛
0.90
0.800.75
0.950.90
0.800.75
0.950.90
0.800.75
>20 cycles
dt
v ( . .)p u
t ( )s
(a)
(b)
(c)
How to Solve This?
• Mixed Integer Nonlinear Programming
• Large Discrete Search Space
• The bottleneck is in time-domain
calculations
• A population based meta-heuristic in
parallel:
• No cross communication required during
parallel calculations
22
Ind
ivid
ua
l n
Start Read system data & cost functions
Find all violating dynamic events
Initialize population (type, size, location)
Solve boosted
voltage PF (6)-(12)
Calculate cost (1)
Calculate individual n
fitness (5) and penalties
... ...
Terminate?
Perform crossover, mutation and elitism
Display optimum types, sizes,
locations and objective valuesEnd
Send to parallel computing cluster
Intialize dynamic
components (13)
yes
no
Calculate
(2) and
penalties
(14)-(18)
Fault N-1
Calculate
(3) and
penalties
(14)-(16),
(19)-(21)
Calculate
(4) and
penalties
(14)-(16),
(22)
Load Step
Ind
ivid
ua
l N
, N
=|P
opu
lati
on|
Ind
ivid
ua
l 1
Parallel Implementation
23
256 IndividualsEach 22 T.D (~15 sec each)
~23.5 hours total
GAOperations~5 seconds
Generation n+1Generation n
25
6 C
ore
s
~5s~5.5
minutes
Generationn
(1) Ignoring communication latency
(2) Each individual takes (roughly) the same time
Speedup Estimation
• Within the parallelizable fraction of code:
• O(n) reduction (linear speedup):
• But not all is parallelizable. Amdahl’s law:
•
• Conservative speedup estimate: 50-Fold (2 Months to a day)
24
𝑆𝑓 =𝑡1𝑡𝑝
𝑆 =1
1 − 𝐹) + 𝐹 𝑆𝑓
𝑆𝑓 ≈ 𝑝 = 250
𝐹 ≈ 98.5%
So Using this
• We can solve a problem previously unsolvable:
• No candidate bus restrictions
• No sensitivity analysis
• Simulate more realistic scenarios
• And (later) expand the search space to include device type
• Is it a problem worth solving?
• Let’s put it to the test
25
Test System
26
10
1
2
3
4
5 6
78
9
11
12
13
14
15
16
17
18
19
20
21 22
23
24
25 26
27
28 29
30
3132
33
34
35
36
3738
39
1
2 34
5
6
7
8 9
10
Stressed System
• Original system is “stiff”.
• Stressed by adding constant torque IM loads consuming around 50% of the total system reactive
load.
• The total load becomes 6341.4 MW and 2779.5 MVar.
• AVR of generators 3, 5, 7 and 9 are initialized between 72% and 86% of their maximum regulator
voltages.
• Minimum steady-state base-case voltage magnitude is 0.918 p.u. at bus 15.
• Over-excitation limiters allowing approximately a 10% increase in field current compared to the
base case.
27
Parameters and Base Case Violations
28
Incident Constraint Violations
Fault (135 ms)
Busses 16, 19, 20, 26, 28, 29, 34, 38, 17, 22, 23, 24, 27, 32 and 33
Sustained N-1 Contingency
Lines (2 to 3), (8 to 9), (9 to 39), (15 to 16), (21 to 22) and (28 to 29)
5% Step Load Perturbation
Voltage collapse
Parameter Value Parameter Value
𝑐𝑠𝑡𝑎𝑡 ,𝑓𝑖𝑥𝑒𝑑 26 (MUSD) 𝑡𝑑𝑖𝑠𝑡 1 (s)
𝑐𝑠𝑡𝑎𝑡 ,𝑣𝑎𝑟 0.09 (MUSD/Mvar) 𝛾1⋯𝛾4 𝛾1 > 𝛾2 + 𝛾3 + 𝛾4
𝑐𝑠𝑣𝑐 ,𝑓𝑖𝑥 𝑒𝑑 13 (MUSD) 𝑉𝑚𝑖𝑛 0.9/0.95 (p.u.)
PQ/PV
𝑐𝑠𝑣𝑐 ,𝑣𝑎𝑟 0.03 (MUSD/Mvar) 𝜎 𝜋(rad)
𝑐𝑚𝑠𝑐𝑏 ,𝑓𝑖𝑥𝑒𝑑 4 (MUSD) 𝑇𝑏 ,𝑓 0.333 (s)
𝑐𝑚𝑠𝑐𝑏 ,𝑣𝑎𝑟 0.01 (MUSD/Mvar) 𝑣𝑟𝑒𝑓 ,𝑑𝑒𝑙𝑎𝑦 0.8 (p.u.)
𝑣𝑟𝑒𝑓 0.9 (p.u.) 𝑇𝐿𝑆 5 (s)
𝑡𝑐 ,𝑓 135 (ms) 𝑎𝑝𝑒𝑎𝑘 0.8
𝑇𝛽 120 (s) 𝑎𝑐𝑦𝑐𝑙𝑒𝑠 15 (cycles)
𝑡𝑘 1 (s) 𝑎𝑑𝑖𝑝 0.85
𝑇𝛾 120 (s) 𝑣𝑠𝑠 ,𝑚𝑖𝑛 0.9 (p.u.)
Results: Single Dynamic Objective
29
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Recov. Index
f2 Bus
Size (Mvar)
STAT 0 20 100
117.6 0.3968 28 100 29 240
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Dev. Index
f3 Bus
Size (Mvar)
STAT 0
7 30
130.1 0.1225 15 130 24 30 28 100
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Dev. Index
f4 Bus
Size (Mvar)
STAT 0 24 30
56.5 0.0700 29 20
Studies usually stop here
But Optimums Violate Constraints
30
OBJECTIVES AND
CONSTRAINTS
# Violations for Comb. Of Devices
Cost STAT
Faults N-1 Load None 15 6 1 0 Fault 0 1 0 117.6 N-1 9 0 0 130.1 Load 8 2 0 56.5
Multi-Obj 0 0 0 201.1
Device Options
# Viol
Opt. Set Tot. Cost
(MUSD) f2 f3 f4 Bus
Size (Mvar)
STAT 0
15 100
201.1 0.188 0.140 0.044
20 100 27 110 28 380 29 100
Voltage Response
31
The Rest of This Presentation
1. Multi-Contingency Dynamic VAR Planning
2. Multiple-Type Multi-Contingency Dynamic VAR Planning
3. Dynamic VAR Planning for Rotor Angle Stability Improvement
4. Final Remarks
32
Compensator Costs
33
Expanded Search Space
34
Device Type Installation Size
1 … NBus 1 … N
𝑓1 =
𝑏=1
𝐵
𝜓𝑏𝐶𝑏 𝑖𝑏, 𝑗𝑏
Single Dynamic Objective
35
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Recov. Index f2 Bus
Size (Mvar)
MSCB 3 N/A SVC 2 N/A
STAT 0 20 100
117.6 0.3968 28 100 29 240
Comb.
MSCB
0
15 100
79.1 0.3973
16 30 28 130
SVC 20 100
STAT 29 250
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Dev. Index
f3 Bus
Size (Mvar)
MSCB 0
12 60
23.6 0.1505 15 320 26 250 28 130
SVC 0
15 100
60.7 0.1395 21 30 25 30 28 130
STAT 0
7 30
130.1 0.1225 15 130 24 30 28 100
Comb. MSCB
0
12 60
23.6 0.1505
15 320 26 250 28 130
SVC N/A STAT N/A
Device Options Constr.
Violated
Optimum Set Total Cost
(MUSD)
Dev. Index
f4 Bus
Size (Mvar)
MSCB 0 7 30
13.2 0.0761 21 60 24 30
SVC 0 24 30
27.5 0.0726 29 20
STAT 0 24 30
56.5 0.0700 29 20
Comb. MSCB
0
7 30
13.2 0.0761 21 60 24 30
SVC N/A STAT N/A
Multiple-Type, Multi-Contingency Results
36
Device Options
# Viol
Opt. Set Tot. Cost
(MUSD) f2 f3 f4 Bus
Size (Mvar)
MSCB 4 N/A SVC 2 N/A
STAT 0
15 100
201.1 0.188 0.140 0.044
20 100 27 110 28 380 29 100
Co
mb
MSCB 0
4 100
88.6 0.220 0.144 0.054
15 190 16 100 20 100 24 100 26 50 27 190 28 70
SVC N/A STAT 29 240
Voltage Response
37
Multiple Runs
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 20 40 60 80 100 120 140 160 180 200
Fitn
ess
of
Bes
t C
hro
mo
som
e
GA Generation
GA Convergence for Multiple Runs
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
38
Consistent?
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
180 185 190 195 200
Fitn
ess
of
Bes
t C
hro
mo
som
e
GA Generation
GA Convergence for Multiple Runs
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
• Cheapest solutions are always
distributed and with many MSCB
combined with one STATCOM
39
The Rest of This Presentation
1. Multi-Contingency Dynamic VAR Planning
2. Multiple-Type Multi-Contingency Dynamic VAR Planning
3. Dynamic VAR Planning for Rotor Angle Stability Improvement
4. Final Remarks
40
Rotor Angle & Voltage Stability
• Highly interrelated in the short-term timescale
• Studies focus on dynamic VAR compensation for FIDVR
• VSC-based compensation (STATCOM), voltage
independent support
• Can rely on impedance to boost voltage and improve
rotor angle performance
• Can we optimize for “fault-on” performance in addition
to FIDVR? 41
Problem Formulation: Objectives
0
1
B
b v b
b
C k c c MVAR
1 ,
1
1max
F
b b f
f
S TF
2
1 1
1 1
2
c
f
tF Jj j
j f n
f j t
S M t dtF
minimizing overall angular oscillations by minimizing
the total kinetic energy deviation during the fault-on
condition
1 2 1 3 2minimize C S S
42
Problem Formulation: Constraints
, 0G LP P P V
, 0G LQ Q Q V
min max
G G GP P P min max
G G GQ Q Q min maxV V V
max,l lS V S
min max
b b bMVAR MVAR MVAR
0 0, 0initf x y ( , , )
dxf x y u
dt
0 ( , , )g x y u
43
Test System and Solution Method
10
1
2
3
4
5 6
78
9
11
12
13
14
15
16
17
18
19
20
21 22
23
24
25 26
27
28 29
30
3132
33
34
35
36
3738
39
1
2 34
5
6
7
8 9
10
For
eac
h in
div
idua
l
Start
Read system and cost data
Initialize population
Solve PF (5)-(11)
Calculate cost (1)
Calculate individual n fitness (4) and penalties
Terminate?
Perform crossover, mutation and elitism
Display optimum sizes, locations and
objective values
End
Send to parallel computing cluster
Intialize dynamic components (12)
yes
no
Run T.D. simulation, calculate (3-4)
and penalties (13)-(14)
44
Study Cases
STATCOM Alone Hybrid STATCOM/Fixed C
FIDVR only Case A Case B
FIDVR and Rotor-Angle Case C Case D
45
Results
Table I
Case Bus
Installed MVAR Cost
PercentChange
Mean Voltage
Recovery(sec)
Rotor-AngleStability
ImprovementC STAT
A
20
None
200
Base 0.581 2.75%24 130
28 170
29 560
B
16 50 100
-16.3% 0.532 3.33%20 80 150
28 60 110
29 200 410
C
20
None
790
31.9% 0.599 8.58%26 100
28 330
29 370
D
20 320 630
19.5% 0.355 8.50%23 100 200
28 60 110
29 200 410
46
STATCOM Alone Hybrid STATCOM/Fixed C
FIDVR only Case A Case B
FIDVR and Rotor-Angle Case C Case D
Results
STATCOM Alone Hybrid STATCOM/Fixed C
FIDVR only Case A Case B
FIDVR and Rotor-Angle Case C Case D47
Results
STATCOM Alone Hybrid STATCOM/Fixed C
FIDVR only Case A Case B
FIDVR and Rotor-Angle Case C Case D48
Results
STATCOM Alone Hybrid STATCOM/Fixed C
FIDVR only Case A Case B
FIDVR and Rotor-Angle Case C Case D49
Conclusion
• Substantial additional installation required to enhance rotor-angle
stability index
• Hybrid (static with VSC-based) installations result in simultaneous
cost reduction and performance enhancement
• At the expense of limiting STATCOM inductive regulation range
50
The Rest of This Presentation
1. Multi-Contingency Dynamic VAR Planning
2. Multiple-Type Multi-Contingency Dynamic VAR Planning
3. Dynamic VAR Planning for Rotor Angle Stability Improvement
4. Final Remarks
51
What Have People Done? (Repeated)
52Also, test systems usually not stressed enough and/or without IM or OXL
Recent PhD Theses Future Work (Repeated)
20071. Consideration of other stability/security
constraints. This research has focused on the reactive power control planning to increase the voltage stability margin and to mitigate the transient voltage dip. Other stability/security constraints such as transient stability and post-contingency bus voltage magnitude requirements may also be included in the optimization formulation of the reactive power control planning.
2. Economic benefit analysis and cost allocation. The planned reactive power control devices are intended to serve as control response for contingencies. Further research on quantifying the economic benefit of these devices and efficiently allocating the investment cost under is challenging but important.
20151. Comparing the effectiveness of
different types of dynamic VARsupport strategies and their cost/benefit assessment.
2. Utilization of reactive support from geographically distributed, power electronics based distributed generation (DG) resources.
3. Improvisation in the dynamic optimization procedure through parallelization,multistart algorithms.
53
Summary of Thesis Contributions
1. In line with the current industry trend, a platform for running massive multi-timescale
parallel simulations is developed and employed for the dynamic VAR planning
problem.
2. A comprehensive solution to dynamic VAR planning is found that achieves necessary
speed without sacrifices in model fidelity under a variety of realistic scenarios.
3. Cost/benefit analysis show significant investment cost reduction compared to the
latest literature, while performance measures are guaranteed.
4. Multiple types of stability phenomena are evaluated simultaneously.
54
Future Work
1. Multi-level parallelization and real-time solutions:
• Commercial software
• Combined component design and system planning (e.g. microgrids)
• Forecasting, and design with uncertainty
• Detecting causality
2. Secondary voltage control and energy management
3. Renewable and storage integration
4. Improvement in the optimization algorithms
55
Thank you!
56
