Islanding¶

Islanding is the ability to model a grid that has split into several disconnected islands, each anchored by a different grid-forming source. Without islanding support, a standard energy-flow solver requires the grid to be fully connected to a single slack node; any bus unreachable from that node is dropped from the solve as ignored. With islanding enabled, every connected island is solved simultaneously, with each island’s own slack node absorbing the local supply–demand imbalance.

monee implements islanding as a set of mixed-integer (MIP) constraints that are added on top of the carrier’s normal steady-state equations. Any solver back-end that supports integer variables can be used (GEKKOSolver or PyomoSolver).

Grid-forming nodes¶

A grid-forming node is a junction that can act as the slack bus of its island. Any junction whose child list contains at least one component that inherits from GridFormingMixin is classified as grid-forming for that carrier.

Carrier	Grid-forming child	Role
Electricity	`ExtPowerGrid`	External grid connection (always)
Electricity	`GridFormingGenerator`	Islanded generator (islanding only)
Gas / Water	`ExtHydrGrid`	External hydraulic connection (always)
Gas / Water	`GridFormingSource`	Islanded compressor / source (islanding only)

GridFormingMixin is a pure marker mixin — it carries no equations. Its sole purpose is to let find_ignored_nodes identify which nodes anchor each island.

Connectivity-flow formulation¶

Reachability from a grid-forming node is enforced by a single-commodity virtual flow model. A virtual super-source node “0” injects flow into every grid-forming junction; the flow propagates through the carrier topology until each energised junction has received exactly one unit.

The binary variable \(e_i \in \{0,1\}\) indicates whether junction \(i\) is energised (\(e_i = 1\)) or de-energised (\(e_i = 0\)).

Variables¶

Variable	Domain	Meaning
\(e_i\)	\(\{0,1\}\)	Junction \(i\) energised
\(c_{ij}^+\)	\(\mathbb{R}_{\geq 0}\)	Connectivity flow on branch \((i,j)\), forward direction
\(c_{ij}^-\)	\(\mathbb{R}_{\geq 0}\)	Connectivity flow on branch \((i,j)\), reverse direction
\(c_i^{\text{src}}\)	\(\mathbb{R}_{\geq 0}\)	Super-source arc into grid-forming junction \(i\)

Constraints¶

Grid-forming junctions are always energised:

\[e_k = 1 \qquad \forall k \in \text{GF}\]

Arc capacity (physical branches): controlled by the branch on/off variable \(x_{ij}\):

\[c_{ij}^+,\; c_{ij}^- \;\leq\; M \cdot x_{ij}\]

Super-source arc capacity (always open for GF nodes, so \(x = 1\)):

\[c_k^{\text{src}} \;\leq\; M \qquad \forall k \in \text{GF}\]

Per-node flow balance: net inflow equals the energisation indicator:

\[\left(\sum_{\text{in}} c\right) - \left(\sum_{\text{out}} c\right) = e_i\]

For grid-forming junctions the super-source arc is counted as additional inflow.

Global super-source supply equals total demand:

\[\sum_{k \in \text{GF}} c_k^{\text{src}} = \sum_i e_i\]

The big-M constant \(M\) must be at least as large as the number of carrier nodes. The default is 200; override via big_m_conn when your network is larger.

Per-carrier physical constraints¶

Beyond the connectivity-flow integers, each carrier mode adds carrier-specific physical constraints to ensure the physical state of de-energised nodes is well-defined for the solver.

Electricity¶

Nodes	Constraint	Why
Grid-forming	\(\theta_k = 0\)	Angle reference for each island
Regular	\(-M_\theta (1 - e_i) \leq \theta_i \leq M_\theta (1 - e_i)\) would force \(\theta_i = 0\) when \(e_i = 0\)	Numerical stability — prevents the angle from floating freely on de-energised buses

The angle reference constraint is strictly necessary for multi-island DC flow: without it the power-flow equations become singular for each island beyond the first (no angle reference defined).

Gas and water¶

Nodes	Constraint	Why
Regular	\(p_i \leq 2\, e_i\)	Forces \(p_i = 0\) when \(e_i = 0\)

The grid-forming junction’s pressure is already pinned to a setpoint by GridFormingSource.overwrite() (or ExtHydrGrid.overwrite()), so no additional constraint is needed at GF nodes.

The pressure bound is primarily useful when switchable pipes are present: a de-energised island with floating pressure can confuse NLP solvers. For networks without switchable pipes the bound is a nice-to-have.

Solver integration¶

Islanding constraints are implemented as a NetworkConstraint — the same interface used by the formulation layer — so they integrate with both solver back-ends without modification.

Phase 1 — prepare(network): Called before the solver injects variables. Adds binary Var placeholders (e_el, e_gas, e_water, etc.) to the node and branch model objects. These are picked up automatically by the standard variable-injection loops.

Phase 2 — equations(network, ignored_nodes): Called after variable injection. Returns the full list of connectivity-flow and physical constraint expressions. The solver appends these to its equation set alongside the normal energy-flow equations.

find_ignored_nodes interaction: When islanding is enabled, find_ignored_nodes uses the complete network topology (all branches, including open ones) and classifies a junction as non-ignored if any of its children is a GridFormingMixin. This prevents island B’s buses from being pruned before the MIP solve even starts.

Class hierarchy¶

NetworkConstraint
└── NetworkIslandingConfig        ← bundles all per-carrier modes
    registered via network.add_extension()

NetworkConstraint (ABC)
└── IslandingMode                 ← per-carrier base class
    ├── ElectricityIslandingMode  ← PowerGrid; angle pinning
    ├── GasIslandingMode          ← GasGrid; pressure bounds
    └── WaterIslandingMode        ← WaterGrid; pressure bounds

ChildModel + GridFormingMixin     ← marker mixin
├── GridFormingGenerator          ← electricity slack generator
└── GridFormingSource             ← gas / water slack source