1. OUTAGE MODELING: PQ BUS NUMERICAL ANALYSIS & RESULTS
Power System Security: The Holomorphic Embedding Method Applied to Post-Outage Analysis
Ibrahima Niang1, Rui Yao2 , Kai Sun3
1 Columbia University, 2, 3 University of Tennessee, Knoxville
INTRODUCTION
OUTAGE MODELING: PQ BUS
Define base state of the system (before outage) for n polynomials coefficients:
Goal: If there is outage of branch will change assuming system does not separate.
Therefore: where is a row vector corresponding to the starting bus of the tripped branch and the ending bus and is the admittance matrix.
HEM APPROACH
where
Using Woodbury Matrix identity, we get the following:
So, and
The outage model updates in case a line is tripped.
The power-flow (PF) study obtains complete voltages angle and magnitude information for each bus in a power system for specified load and generator real power and voltage conditions.
Due to the nonlinear nature of this problem, numerical methods are employed to obtain a solution that is within an acceptable tolerance
The Holomorphic Embedding Method (HEM) and the PF statements and algorithms both solve the PF problem. But, the PF method has convergence issues (closeness of the voltage collapse point of the system loading)
The traditional PF method uses iterative techniques such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and the HEM uses recursive techniques
Cascading Outages:
Consequences: Catastrophic economic and social impacts
Characteristics: faults, power swing, overload…
Protection Relay Operations: Trip Lines, Generators, loads…
NUMERICAL ANALYSIS & RESULTS
HEM MODELING [1]
Three bus system diagram
CHARACTERISTICS
Implicit Function
where 1 is a slack bus, and 2 and 3 are PQ buses
Embedded System
where I is the current between bus 1 and bus 2
The inverse of the voltage series coefficients
Maclaurin Series Representation
Recursive relation between V(n) and W(n)
CONCLUSION
MULTI-BUS HEM PQ MODEL
We implement the traditional HEM method in MATLAB.
We propose and develop the novel HEM method for post-outage power flow calculation based on the efficient rank-1 update of impedance matrix.
Based on the numerical results we can see that our method exactly matched the results obtained from the Newton Raphson method
The series branch of Y matrix
Embedded model for N PQ Bus
MULTI-BUS HEM PQ&PV MODEL
Future Works
Voltage Power Series Equation
Embedded model for N PQ/PV Bus
First, complete the outage modeling for a PV bus systems only and a PV&PQ bus systems.
Next, test the performance of the proposed method on larger systems.
Delta Function
General Equation in Matrix Form
References
[1] S.D. Varwandkar, Jeremy Lin, "Direct determination of load flow quantities from PQ injections: A new formulation", International Journal of Electrical Power & Energy Systems, vol. 89, pp. 19, 2017, ISSN
This work was supported primarily by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC
Other US government and industrial sponsors of CURENT research are also gratefully acknowledged.