Optimal Usage of Transmission Capacity with FACTS Devices
In the Presence of Wind Generation
Rui Yang and Gabriela Hug-Glanzmann
ruiy@andrew.cmu.edu, ghug@ece.cmu.edu
Department of Electrical and Computer Engineering, Carnegie Mellon University
Offline Simulation
Simulation Results
 Optimization Problem Formulation
• No overloading
• Control variable
Wind Speed
(m/s)
1
Poor
0-200
0.0-5.6
Marginal
3
200-300
Fair
4
300-400
Good
5
400-500
Excellent
500-600
5.6-6.4
6.4-7.0
7.0-7.5
X TCSC ,n
• Objective function
• Maximizing the minimum value of the capacity margin
max (min ( Pm arg in ,ij )),
where Pm arg in ,ij =
F
7.5-8.0
6
Outstanding
600-800
8.0-8.8
7
Superb
>800
>8.8
• Areas with high availability of wind ≠ demand centers
• Constraints
• Power flow equations
− Pij
max
ij
F
PG ,i − PL ,i − ∑ Pij= 0, QG ,i − QL ,i − ∑ Qij= 0
• Limits of the device settings
• Variable power output of the wind generators
max
ij
j
 Determining Key Measurements
 Potentials of FACTS Devices
• Active power flow and current magnitude of each line
• Redirect the network flows and regulate nodal voltages
• Voltage angle at each bus
• Allow better usage of the current transmission facilities
• Current setting of the FACTS device
• Able to deal with the rapid fluctuations of the wind generation
 Regression Analysis
 Proposed Solution
• Polynomial fitting - a sparse solution for the coefficients wanted
• Use FACTS devices to render the system more flexible
• Formulate a L0-norm regularization problem
A Two-stage Approach
• A subset of important coefficients is identified
• Develop a scheme which determines the optimal steady-state settings of
the FACTS devices with respect to certain objectives only using a limited
amount of information
 Proposed Method – A Two-stage Approach
• The optimal tradeoff between the fitting accuracy and the
number of measurements used is achieved
Offline
Simulation
Optimal Power
Flow (OPF)
Optimal Device
Settings
Regression
Analysis
Function
Load/Generation
Scenarios
Measurements
Selection
Key
Measurements
Online
Operation
Controller
Values from Key
Measurements
 Offline Simulation
• Solve OPF for various generation and load scenarios
• Determine function: optimal setting = f(key measurements)
 Online Decision Making
• Evaluate the locally stored function
• No online OPF calculations needed
System Setup
 System Setup
Optimal
Device
Setting
• IEEE 14-bus system
• Wind generator at Bus 2
• Load center on north side
 Simulations
• 1000 different load/generation
scenarios
0.02
0.6
0
0.4
0.1
Actual
0.2
Estimated
0
200
400
600
800 1000 1200
Load and Generation Scenarios
0
200
400
600
800 1000 1200
Load and Generation Scenarios
Relative Error in the Objective Function
1400
0
200
1400
0.05
0
1400
400
600
800 1000 1200
Load and Generation Scenarios
• Overloading
Error in the Objective Function
Objective Function
0.4
0.08
0.3
0.07
0.2
0.06
0.1
0.05
0
-0.1
-0.2
0
100
200
300
400
Load and Generation Scenarios
0.04
0.03
0.02
Actual
Estimated
Without TCSC
-0.3
-0.4
• Orthogonal Matching Pursuit (OMP)
 Objective
0.8
0
j
−0.9 X Line,n ≤ X TCSC ,n ≤ 0.4 X Line,n
0.04
Without TCSC
0.01
0
500
0
100
200
300
400
Load and Generation Scenarios
 Two – TCSC – Case
1
0.1
0.8
0.08
0.6
0.4
Actual
Estimated
Without TCSC
0.2
0
0
200
400
600
800 1000 1200
Load and Generation Scenarios
500
Error in the Objective Function
Objective Function
Minimum Capacity Margin (p.u.)
2
• Setting of the FACTS devices
Error in the Objective Function
1
Error (p.u.)
Density
(W/m2)
Relative Error
Potential
Error (p.u.)
Class
Objective Function
Error (p.u.)
 Challenges
 One – TCSC – Case
Minimum Capacity Margin (p.u.)
 Accelerated Integration of Wind Energy Resources
Minimum Capacity Margin (p.u.)
Motivation
0.06
0.04
0.02
1400
0
0
200
400
600
800 1000 1200
Load and Generation Scenarios
Conclusions and Future Work
 Conclusions
• 800 scenarios for training
• Usage of regression analysis provides solution to determine close-tooptimal settings of the FACTS devices
• 200 scenarios for testing
• Proposed approach provides fast online operation without solving OPF
• One TCSC in the system – TCSC in Line 1-2
• Two TCSCs in the system – TCSC1 in Line 1-2 and TCSC2 in Line 2-5
 Future Work
• Further investigation with larger system
1400