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Time Series Based Semi-Analytical Solution of Power Systems and its Application in Direct Methods
Eric Abreut Bin Wang
- Dr. Kai Sun
Final Presentation July 14, 2016 Knoxville, Tennessee
Stability Problem
2
Time Series Based Semi-Analytical Solution of Power Systems and its - - PowerPoint PPT Presentation
Time Series Based Semi-Analytical Solution of Power Systems and its - - PowerPoint PPT Presentation
Time Series Based Semi-Analytical Solution of Power Systems and its Application in Direct Methods Eric Abreut Bin Wang Dr. Kai Sun Final Presentation July 14, 2016 Knoxville, Tennessee Stability Problem 2 Time Domain Simulation vs. Direct
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Time Domain Simulation vs. Direct Method Simulation
- Time Domain Simulation:
◖ Numerical solution of the nonlinear differential algebraic equations. ◖ Time consuming. ◖ No information on the stability margin.
- Direct Method Simulation:
◖ Evaluation of the predefined energy function for a power system. ◖ Almost Real-time. ◖ Stability margin is determined.
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Traditional Direct Method Principle
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Proposed Method
- Traditional direct method includes fault-on time domain simulation (TDS).
- Proposed method removes fault-on TDS and replaces with the fault-on
symbolic semi-analytical solution.
- This makes the method faster than real-time.
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Why it is Useful
- Help determine stability close to real time.
- Provide explicit analytical solution.
- Solution can replace Time Domain Simulation for short-time trajectory of
system.
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Formula and Steps Used
Step 1: Where a10 through anm are unknown variables . Total number of unknowns are (m+1)*n.
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Formula and Steps Used
Step 2:
Substitute assumed solution into given differential equations.
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Formula and Steps Used
Step 3:
Equate the two sides of DE’s term by term for each equation:
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Formula and Steps Used
Step 4:
Solve for the unknowns.
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IEEE 9-bus System
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Current Results
- Blue Curve (under Red Curve) is from the time domain simulation.
- Red Curve (above Blue Curve) is from the proposed method.
- Results are accurate.
This simulation is for a three-phase fault at BUS 7 for IEEE 9-BUS system. This figure is showing the fault-on trajectory of the system.
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CCT = Fault Time Duration
CCT = .231 Error Index = .492 degrees CCT = .430 Error Index = 19.936 degrees
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ACCURACY TABLE
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Decoupling Based Direct Method
- Linear decoupling transformation.
- Single machine infinite bus (SMIB) power systems as oscillation
modes are constructed.
- Transient energy function method is applied to each SMIB system.
- Stability margins are calculated.
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Small System Stability Margin and CCT Ranking Table
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Large System Introduction
- Fault-on Duration was set to .05 seconds for all cases.
- If CCT > FDT then the system should be stable.
- However, if CCT < FDT then the system should be
unstable.
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Large System Stability Margin and CCT Ranking Table
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Large System Stability Margin and CCT Ranking Table
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Next Steps
Prepare and submit General Meeting paper by October.
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Acknowledgements
This work was supported primarily by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC-1041877. Other US government and industrial sponsors of CURENT research are also gratefully acknowledged.
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