Spanning Tree

Every spanning tree in a distribution feeder has exactly one root node: the substation bus. Power flows outward from this source along a unique path to each load node. This property simplifies fault detection—when a fault occurs, the path from the substation to the fault location is unambiguous. Key implications include:

• Voltage profile degrades monotonically along each branch as distance from the source increases
• Protection zones are inherently directional, with devices coordinated from the substation outward
• Service restoration algorithms search for alternative source nodes (adjacent feeders) to re-root the spanning tree for de-energized customers

The single-source constraint differentiates distribution spanning trees from generic graph theory spanning trees, which may have arbitrary root placement.

A Normally Open Point (NOP) is a tie switch that remains open during normal operation, physically connecting two feeders or lateral branches but electrically separating them to preserve radiality. NOPs are the critical boundary elements between adjacent spanning trees. Their strategic placement determines:

• Load transfer capability during emergencies—closing an NOP and opening a faulted segment restores customers from an alternative source
• Reconfiguration flexibility for loss minimization, as NOPs provide candidate switching locations
• Cold Load Pickup (CLPU) risk, since closing an NOP onto a long-de-energized feeder segment may trigger inrush currents exceeding protection settings

Modern Soft Open Points (SOPs) replace mechanical NOPs with power electronics, enabling continuous active and reactive power flow control between spanning trees without violating radiality.

In a spanning tree, exactly one path exists between any two nodes. This unique path property is the foundation of distribution protection schemes. When a fault occurs at a specific node or line segment, the fault current flows along a single, predictable route from the substation. Protection engineers exploit this to:

• Set time-current coordination curves so the nearest upstream device trips first
• Implement fault isolation logic that opens the two switches immediately adjacent to the faulted segment
• Design self-healing grid automation that rapidly identifies the faulted zone and reconfigures the spanning tree to bypass it

The absence of alternative paths eliminates the complex directional comparison schemes required in meshed transmission networks, dramatically simplifying relay settings.

The Branch Exchange Method is a heuristic optimization technique that exploits spanning tree properties to minimize losses. The algorithm:

1. Starts with a valid radial spanning tree
2. Closes a single NOP, temporarily creating exactly one loop
3. Calculates the loss reduction from opening each switch in that loop
4. Opens the switch that yields the greatest loss reduction, restoring radiality

This process iterates until no further loss improvement is found. The method guarantees radiality at every step because each iteration exchanges exactly one closed branch for one open branch. More advanced formulations use Mixed-Integer Linear Programming (MILP) to solve for globally optimal spanning trees across multiple feeders simultaneously, incorporating voltage constraints and load balancing objectives.

The N-1 Criterion requires that the failure of any single component—such as a feeder breaker or transformer—does not cause sustained customer outages. For spanning trees, this translates to ensuring every load node has access to at least one alternative source via NOP connections to adjacent trees. When a source fails:

• The affected spanning tree is partitioned into isolated sub-trees
• Service Restoration (SR) algorithms search for healthy adjacent feeders with sufficient spare capacity
• NOPs are closed to re-root de-energized sub-trees onto alternative sources, creating new valid spanning trees

This re-rooting must respect thermal limits and voltage constraints of the new source path. System Average Interruption Duration Index (SAIDI) directly reflects how efficiently a utility's spanning tree topology supports N-1 reconfiguration.