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 01420615 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.