Busbar Splitting in Power Systems

• Busbar splitting is defined as the reconfiguration of a single busbar into multiple, electrically distinct sections via switch or breaker actions, enabling different voltage levels and phase angles.
• It is used in grid topology optimization to redistribute lines, generators, and loads, thereby reducing generation cost, relieving congestion, and enhancing contingency response.
• In conductor design, busbar splitting replaces a single massive conductor with parallel bars to improve current sharing, manage thermal loads, and fine-tune electromagnetic properties.

Busbar splitting denotes a reconfiguration in which a busbar that normally operates as a single electrical node is partitioned into two or more electrically separate sections by operating switches or circuit breakers. In transmission-operation and optimization literature, the split sections become distinct buses with potentially different voltage magnitudes and phase angles in AC systems, or different DC voltages in DC grids; in busbar-system design literature, the same phrase can also denote replacing one “solid” bus with several parallel busbars. Recent work treats the first meaning as a fully fledged topological control action, on equal footing with optimal transmission switching, rather than merely a maintenance detail of substation design (Bastianel et al., 2024).

1. Definitions, physical realization, and scope

In the substation-topology sense, busbar splitting is the operation of opening a busbar coupler so that one “logical bus” becomes two distinct nodes. Before splitting, all connected elements share one voltage magnitude and one voltage angle in AC models, or one DC voltage in DC models. After splitting, the sections are physically close but electrically distinct, and lines, transformers, generators, loads, and converters can be redistributed between them. This increases the electrical distance between elements that were previously at the same node and changes the power-flow pattern. Operationally, double-bus, double-bus double-breaker, breaker-and-a-half, and ring-bus arrangements provide the switching flexibility needed for such actions (Bastianel et al., 2024, Zhou et al., 2020).

A common abstraction is to split a busbar $i$ into $i$ and $i'$, reroute each original element through an auxiliary bus, and connect that auxiliary bus to either $i$ or $i'$ through switches. A zero-impedance link represents the bus coupler that can be opened or closed. In this representation, the busbar configuration is encoded by binary switch variables, while the zero-impedance link determines whether the two sections are electrically identical or separate (Bastianel et al., 2024).

A second, distinct usage appears in analytical and numerical modeling of busbar systems. There, busbar splitting means replacing one conductor by several parallel massive rectangular conductors, either adjacent or non-adjacent, in order to manage current sharing, electrodynamic forces, inductance, and thermal behavior. The underlying problem is then not network topology optimization but the electromagnetic behavior of multi-bar arrangements under normal and fault currents (Giaccone et al., 2014).

2. Topological and algebraic representations

Within linear power-flow theory, busbar splitting can be formulated as a change in the grounded Laplacian $B$ of the network. Under the DC approximation, the standard relations are

$$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$

where $p$ is the nodal injection vector, $\theta$ the vector of bus phase angles, $f$ the vector of branch flows, $i$0 the incidence matrix, and $i$1 the grounded Laplacian. Recent work introduces bus merge and bus split distribution factors in the same low-rank-update framework that already contains PTDFs, LODFs, LCDFs, and PSDFs (Dijk et al., 2024).

For a bus split, the literature distinguishes three configurations: a merged configuration $i$2, a closed but unmerged configuration $i$3, and an open configuration $i$4. The busbar coupler is modeled as a branch with susceptance $i$5, closed when $i$6 and open when $i$7. Using Sherman–Morrison and Woodbury identities, the inverse grounded Laplacian of the open topology can be obtained from the closed configuration without explicitly solving a new full DC power flow. The resulting post-split PTDF takes the form

$i$8

with the bus split distribution factor vector

$i$9

This formulation places bus splitting on the same algebraic footing as line outages and simultaneous switching events. It also yields an islanding criterion: $i'$0 which identifies bus splits that disconnect the grid (Dijk et al., 2024).

A different but related representation appears in substation-level topology optimization under DC power flow. There, splitting bus $i'$1 and reconnecting a single line $i'$2 and a net injection to a new bus $i'$3 is represented in the bus-branch model as opening line $i'$4 and introducing an additional power transfer between buses $i'$5 and $i'$6. This equivalent formulation avoids explicit breaker-level enumeration while preserving the impact of the split on nodal balances and line constraints (Zhou et al., 2020).

3. Optimization formulations in AC, DC, and hybrid AC/DC grids

In hybrid AC/DC grids, busbar splitting has been formulated as part of a joint OTS/BS problem whose objective is to minimize total generation cost,

$i'$7

The formulation extends a hybrid AC/DC OPF with split-node sets for AC and DC buses, auxiliary buses for rerouted elements, and binary switch variables for AC and DC busbar switches. In the exact formulation, a closed AC busbar switch enforces

$i'$8

and a closed DC switch enforces

$i'$9

An exclusivity constraint,

$i$0

ensures that each element is connected to at most one part of the split busbar; in the joint OTS/BS model, the inequality allows the element to be disconnected entirely if OTS is also active (Bastianel et al., 2024).

To avoid bilinear products such as $i$1 and $i$2, a big-$i$3 reformulation is used. For AC busbar switches,

$i$4

$i$5

For DC switches,

$i$6

When the switch is closed, the equalities are enforced; when it is open, the voltage difference is bounded only by the chosen big-$i$7 constant (Bastianel et al., 2024).

The same work evaluates three relaxations or approximations for the continuous part of the model while keeping identical binary topology decisions: SOC, QC, and LPAC. In the SOC and QC models, voltage products are lifted to $i$8-variables; in LPAC, voltage magnitude deviations $i$9 are used and the result is a MILP. The continuous relaxation changes, but the busbar-switch logic remains encoded through big-$i'$0 constraints adapted to the lifted or linearized variables (Bastianel et al., 2024).

A complementary DC-based formulation models bus splitting jointly with line switching and then removes the induced bilinear terms by an exact McCormick reformulation. Because the binary factors are multiplied by bounded continuous generation variables, the McCormick envelopes are tight, so the mixed-integer linear reformulation is exact rather than approximate (Zhou et al., 2020).

4. Economic impact, computational tractability, and candidate selection

On the 5-bus AC plus 3-bus DC hybrid test case, splitting AC busbar 2 reduced the objective from $i'$1 in the original AC-BS MINLP and to $i'$2 in LPAC space and an AC-feasible solution of $i'$3. On larger hybrid cases with 39, 67, 588, and 3120 buses, splitting one AC busbar consistently lowered generation cost in both AC-BS and LPAC-BS, whereas splitting one DC busbar helped in some cases and had no impact in others. In all BS simulations where OTS was enabled, no element ended up fully disconnected; the optimizer used BS as a reconfiguration tool rather than as a way to shed elements (Bastianel et al., 2024).

The tractability gap between formulations is substantial. Exact AC-BS big-$i'$4 required tens to hundreds of seconds on the 5-bus case and up to 3.5 hours for a single split on the 3120-bus case. LPAC-BS was typically 10–30× faster than AC-BS big-$i'$5, while SOC- and QC-BS were very fast on small cases and provided useful lower bounds but were not always AC-feasible when re-checked against the original model. This suggests a two-level workflow in which approximate or relaxed models screen candidate actions and exact AC formulations validate a smaller set of promising topologies (Bastianel et al., 2024).

Because exhaustive single-bus screening is already expensive, recent work proposes metrics for ranking promising busbars. One metric is

$i'$6

the sum of absolute LMP differences across all branches incident to bus $i'$7. Additional metrics are $i'$8, the number of congested incident branches, and $i'$9, an indicator for binding voltage magnitude or angle constraints. On a 793-bus system, exhaustive one-bus-at-a-time BuS optimization took about 19.14 hours, whereas a metric-based selection of 15 buses reduced the time to about 0.98 hours. On a 3374-bus system, exhaustive testing took about 374.98 hours, while 20 selected buses required about 3.77 hours (Bastianel et al., 14 Oct 2025).

Learning-based acceleration has been proposed for still larger search spaces. A heterogeneous edge-aware message passing neural network was trained to predict effective busbar splitting actions as candidate network topology optimization solutions. On the GOC 2000-bus system, the reported results were AC-feasible solutions within one minute and a $B$0 optimality gap, together with up to 4 orders-of-magnitude speed-up. This suggests that candidate metrics and GNN-based ranking are not competing abstractions but complementary mechanisms for shrinking the mixed-integer search space before a final AC-feasibility check (Rajaei et al., 23 Oct 2025).

5. Security-constrained formulations and voltage-sensitive analysis

A recurrent misconception in operational studies is that a substation with a closed coupler can always be collapsed to a single bus without loss of relevant security information. Security-constrained substation reconfiguration work explicitly rejects that simplification for $B$1 coupler and busbar contingencies. In that setting, the optimization must choose coupler status $B$2 and assignment variables for lines, generators, and loads even when the coupler is closed, because those assignments determine the post-contingency topology if the coupler trips or one busbar is lost. The resulting MILP incorporates line, coupler, and busbar contingencies, linear AC power flow, reserve deployment, and load shedding (Rajaei et al., 4 Mar 2026).

The objective combines normal-state dispatch and reserve cost with contingency load-shedding cost. A heuristic with multiple master problems decomposes the problem into a central dispatch master problem and independent substation master problems solved in parallel, plus feasibility and optimality sub-problems for contingencies. On the IEEE 118-bus case, this HMMP reduced expected energy not served from about $B$3 of total load in the baseline to about $B$4, with a $B$5 improvement in the objective in 19 seconds. On the PEGASE 1354-bus case, average load-shedding cost fell from 2110.4 k€ to 820.5 k€, average load shedding per contingency from 211 MW to 82 MW, and average ENS from $B$6 to $B$7 (Rajaei et al., 4 Mar 2026).

A second limitation of classical DC sensitivities is that they cannot represent voltage magnitude changes, reactive power, or losses, all of which matter for busbar splitting. Voltage-sensitive generalized distribution factors derived from a linearization of the full AC power-flow equations address this gap. The resulting “DC+” model updates the linearized AC Jacobian $B$8 through low-rank matrix identities and produces generalized PTDF-, LODF-, and line-modification-like factors for topology changes, including busbar coupler opening. In a busbar splitting example at a 225 kV substation, full AC power flow gave a voltage drop at one busbar from 225 kV to 198 kV and an angle change from about $B$9 to $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$0, while the AC-linearized bus split factor predicted 201 kV and $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$1. This directly illustrates why DC PTDFs are incomplete for detailed busbar splitting studies (Titz et al., 24 Sep 2025).

6. Event identification, contingency screening, and protection contexts

Bus split events can also be treated as a topology-identification problem. Under a DC bus-branch model, a bus split is represented by binary connectivity variables indicating which lines, generators, and loads move from bus $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$2 to a new bus $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$3. The identification problem matches predicted changes in bus phase angles, and optionally line flows, to synchrophasor measurements. By introducing an auxiliary inverse matrix and then replacing binary-continuous products through McCormick constraints, the bilinear formulation becomes an MILP. On the original IEEE 300-bus case, the reported average identification accuracy was about $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$4; on a modified 300-bus case with lower line resistances it rose to about $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$5. Under partial PMU coverage, the reported average accuracies were about $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$6, $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$7, and $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$8 for three measurement configurations (Zhou et al., 2020).

At a more structural level, grid splitting can be identified through graph connectivity. In a graph model $$p = B\theta, \qquad f = PTDF \cdot p, \qquad PTDF := B E^\top B^{-1},$$9, a branch whose removal increases the number of connected components is a bridge. Fast bridge detection therefore screens $p$0 contingencies for islanding or splitting cases. A graph-computing BFS implementation on a real China State Grid system with 2752 buses and 3290 edges reduced runtime from 1350 ms for an adjacency linked-list Tarjan implementation to 205.54 ms, a reported speed-up of about 6 times (Zhu et al., 2019).

Busbar splitting also intersects with wide-area protection. Controlled system separation treats breaker operations at lines, transformers, bus couplers, and tie-lines as a deliberate last-resort action when loss of synchronism is detected. A PMU-based detector using generator rotor angles, frequencies, center-of-inertia coordinates, and kinetic energy addresses the “when to split?” problem, while candidate generator groupings and predefined cutsets address the “where to split?” problem. In the IEEE 39-bus demonstrations, the selected actions were specific breaker openings such as line 14–15 or line 16–24, which are the practical implementation of system splitting through busbar and corridor reconfiguration (Tyuryukanov et al., 2022).

7. Busbar splitting in conductor-system design

In busbar-system design, busbar splitting means that one phase or pole is realized by several parallel rectangular conductors rather than one thick bar. The analytical framework of Canova and Giaccone models massive conductors with homogeneous current density, $p$1, where $p$2 and $p$3 are the conductor width and height. Within this usage, busbar splitting is motivated by current sharing, electrodynamic force reduction under short-circuit, inductance tuning, redundancy, and thermal management (Giaccone et al., 2014).

The central problem is the force and inductance interaction between adjacent or non-adjacent conductors. The corrected fourfold integrals for the force components are written over the two conductor cross-sections, and the errata correct auxiliary terms

$p$4

as well as a closed-form term to

$p$5

For non-adjacent formulas, the stated range of validity is strict: $p$6 The accompanying MATLAB tools are adjacent.m, NonAdjacentX.m, and NonAdjacentY.m (Giaccone et al., 2014).

This literature uses “busbar splitting” in a materially different sense from the OPF and topology-optimization literature. There, the questions are electromagnetic force, inductance, and fault-current behavior of multi-bar arrangements; in transmission-topology studies, the questions are congestion relief, economic dispatch, contingency response, and topology identification. The shared term refers to a common physical intuition—partitioning what would otherwise be a single busbar entity—but the models, variables, and performance criteria are different (Giaccone et al., 2014).

Busbar splitting therefore occupies two adjacent but distinct positions in power-system research. As a substation reconfiguration, it is a controllable topological action represented through binary coupler and assignment variables, low-rank updates of network matrices, or generalized AC sensitivities, and it is used for congestion management, security-constrained operation, and topology identification (Bastianel et al., 2024). As a conductor-design problem, it is the decomposition of one current-carrying bar into several massive conductors, analyzed through force and inductance formulas under explicit geometric assumptions (Giaccone et al., 2014). Across both meanings, the central technical theme is the same: partitioning a busbar changes the admissible electrical states, and those changes can be quantified, optimized, or monitored with models tailored to the relevant scale.