A Transformation Technique for Decoupling Power Networks
Iraj Rahimi Pordanjani, Yunfei Wang, and Wilsun Xu,
University of Alberta Department of Electrical and Computer Engineering
Overview 2
Introduction The proposed Transformation Decomposition of PV Curves
Potential Applications Summary
Introduction 3
The network wide-area phasors (voltages and currents with synchronized phase angles) are available.
Phasor Measurement Units (PMU): The most accurate and advanced time-synchronized technology available to power engineers
How to use the data for power system analysis and monitoring is still not quite clear.
Introduction 4
Ib
Va
Ia
Vb
Ic Vc
3-phase data
Symmetrical Components Transform
Various monitoring and protection schemes
PMUs data (network wide-area data)
How to make effective use of the data How to use the data
A Support Theory
Power systems analysis and monitoring
Special focus: Voltage stability analysis, and monitoring
Analogy with 3-phase data:
Decompose the data into:
Zero, positive, and negative sequences
The Proposed Transformation 5
A three-phase symmetrical line
The symmetrical components transform is a method for decoupling the above system and is based on the eigen-decomposition of the [Z] matrix of the system
The Proposed Transformation 6
Multiple “phase” view of a power network
A general electric power network
One generator One multi-phase line One load
Phase coupling
Eigen-decomposition:
The Proposed Transformation 7
Conduct a modal transform to decouple the n-phase network into a n de-coupled networks called channel networks.
Then:
A complex network has been transformed into a set of decoupled simple circuits.
By analyzing the decoupled networks, one may extract important information about the actual network.
Decomposition of PV Curves 8
PV curves
Difficult to be obtained
especially in online applications Can be easily obtained.
Actual PV curves Channel PV curves
Decomposition of PV Curves 9
Conceptual case studies: Case study 1
responsible for power transfer
Decomposition of PV Curves 10
PV curves of the actual system Channel PV curve (Channel 1)
The channel PV curve reaches its nose point when the physical PV curves reach their noise points.
Decomposition of PV Curves 11
Case study 2 The same network configuration but unequal impedances
Channel 1 transfers the highest power and the maximum power transfer stops at the nose point of channel 1 PV curve.
Channel 1 is the critical channel.
Decomposition of PV Curves 12
Results for IEEE 30-bus system:
Decomposition of PV Curves 13
Results for IEEE 57-bus system:
Potential Applications 14
Monitoring the stability level by monitoring the critical channel’s margin.
Identification of the critical load by determining the contributions of loads to the critical channel’s load.
Identification of the critical generator by determining the contributions of generators to the critical channel’s voltage source.
...
Summary 15
A transformation has been proposed to convert a complex power system into simple decoupled modal networks.
By analyzing and monitoring the characteristics of modal networks, one can extract important information about the actual system.
This paper has presented the progress made on the voltage stability analysis and monitoring using the proposed transform. It has been shown that the PV curves of decoupled modal networks may be used instead of actual PV curves to monitor the voltage stability.
16
Thanks for your attention
Current Research Progress Critical Load Identification
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Once the critical channel is known, it can be used to identify the critical bus.
The critical load bus is the most responsible for the voltage drop of the critical channel.
Low stability margin
Since the channel voltage drop is caused by the channel current, the contribution of bus currents I to the critical channel current Ji can be used.
Large voltage drop
The bus whose current has the highest contribution to the critical channel current is the critical bus.
Verifications methods:
Modal analysis method
The sensitivity of loadability margin with respect to load shedding at different load buses
Current Research Progress Critical Load Identification
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Bus ranking results in IEEE 30-bus system:
Proposed index
Modal analysis method Sensitivity-based method
Current Research Progress Critical Load Identification
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Bus ranking results in IEEE 57-bus system:
Proposed index
Modal analysis method Sensitivity-based method
Current Research Progress Critical Load Identification
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System Critical channel Critical load bus
Proposed mthod Modal analysis Sensitivity-based
6-bus 1 5 5 5
WSCC 9-bus 1 9 9 9
30-bus 4 8 8 8
IEEE 30-bus 1 30 30 30
IEEE 57-bus 1 31 31 31
AIES 2038-bus 18 630 630 630
Summary of results:
The proposed method can accurately identify the critical bus.