Contingency Analysis

The fundamental reliability planning rule requiring the power system to withstand the failure of any single component—such as a feeder, transformer, or generator—without causing a sustained customer outage. Contingency analysis is the computational process that verifies compliance with this criterion. A system that satisfies N-1 can experience a single contingency and remain within all thermal limits and voltage limits without load shedding.

• N-0: System intact, no contingencies
• N-1: Any single element out of service
• N-2: Any two elements out of service (rarely required for distribution)
• N-1-1: System survives a second contingency before the first is repaired

The emergency control process triggered when contingency analysis detects a violation or an actual fault occurs. SR algorithms find and execute a sequence of switching operations to re-energize de-energized customers by transferring them to healthy adjacent feeders. The objective is to maximize restored load while respecting radiality constraints and thermal limits.

• Fault isolation: Open switches around the faulted segment
• Load transfer: Close normally open tie switches to backfeed
• Reconfiguration: Adjust topology to relieve overloads
• Cold load pickup: Account for inrush current after prolonged outages

A fundamental operational rule in distribution systems requiring the network topology to remain a tree structure without any closed loops. This ensures simple protection coordination and predictable fault current paths. Contingency analysis must verify that any post-contingency reconfiguration maintains radiality.

• Each load bus must have exactly one path to the substation
• Closed loops cause circulating currents and protection miscoordination
• Enforced by spanning tree algorithms in optimization solvers
• Temporary loops allowed during switching sequences if break-before-make

The process of altering the open/closed status of sectionalizing switches and tie switches to transfer load between feeders without interrupting service. DFR is the primary mechanism by which contingency analysis resolves violations. Modern DFR uses mixed-integer linear programming (MILP) or heuristic search to find optimal topologies.

• Normally open points (NOPs): Tie switches kept open for radiality
• Branch exchange method: Iteratively swap switch statuses to reduce losses
• DistFlow equations: Simplified power flow for radial networks
• Multi-objective: Balance loss reduction, switching count, and load balance

The physical constraints that contingency analysis must verify are not violated. Thermal limits define the maximum current-carrying capacity of conductors and transformers before insulation damage occurs. Voltage limits specify the acceptable voltage range at customer service points, typically ±5% of nominal per ANSI C84.1.

• Line ampacity: Function of conductor size, ambient temperature, and wind
• Transformer MVA rating: Cannot exceed nameplate capacity
• Undervoltage: Below 0.95 pu risks motor stalling
• Overvoltage: Above 1.05 pu risks equipment damage
• Conservation Voltage Reduction (CVR): Operate at lower bound to save energy

The temporary surge in demand that occurs when restoring power after a prolonged outage, caused by the simultaneous starting of thermostatically controlled loads like HVAC systems, refrigerators, and water heaters. Contingency analysis must model CLPU to ensure the restoration path can handle the inrush without tripping protection.

• Diversity factor loss: Normal load diversity disappears during outage
• Inrush current: Can be 2-10× normal load for seconds to minutes
• Duration-dependent: Longer outages cause higher CLPU magnitude
• Mitigation: Staged restoration or CVR to reduce initial demand