In this post, I’ll share insights from my current research on robust partitioning for renewable-heavy power networks using submodular optimization techniques—a paper I’m preparing for submission to PSCC 2026.
Renewables and Grid Complexity
Modern power grids are undergoing a fundamental transformation. With increasing integration of renewable energy resources (RERs) like solar and wind, we’re seeing:
- Intermittency and variability from renewable sources
- Decentralized generation replacing traditional centralized plants
- Complex interactions between conventional and inverter-based resources
- Higher vulnerability to cascading failures
Traditional grid partitioning approaches fall short because they rely on simplified linear models or static graph-theoretic methods that don’t capture the dynamic complexity of renewable-heavy systems.
Approach: Control-Theoretic Partitioning
As compared to static topological measures, we propose embedding dynamic control-theoretic measures directly into the partitioning problem. The key insight is to formulate this as a submodular optimization problem.
Submodular Optimization: A Scalable Approach
Submodular functions have a “diminishing returns” property—adding an element to a smaller set provides more benefit than adding it to a larger set. This naturally captures how control and observability benefits decrease as subsystems grow larger.
The Mathematical Framework
We consider a full nonlinear differential-algebraic equation (NDAE) model:
$$ \dot{\mathbf{x}}_d = \mathbf{f}(\mathbf{x}_d, \mathbf{x}_a, \mathbf{u}) $$
$$ \mathbf{0} = \mathbf{g}(\mathbf{x}_d, \mathbf{x}_a) $$
where:
- $\mathbf{x}_d$ are dynamic states (generators, PV plants, motor loads)
- $\mathbf{x}_a$ are algebraic states (voltage angles, magnitudes)
- $\mathbf{u}$ are control inputs
The partitioning problem becomes:
$$ \max_{\mathcal{S}} \quad f(\mathcal{S}) = \sum_{i \in \mathcal{C}} f_i\left({v \in \mathcal{V} \mid (i,v) \in S}\right) $$
$$ \text{subject to} \quad \left|\mathcal{S} \cap (\mathcal{C} \times {v})\right| \leq 1, \quad \forall v \in \mathcal{V} $$
This ensures each bus $v$ belongs to at most one subsystem while maximizing control-theoretic objectives.
Contributions
1. Dynamic Metrics Instead of Static
Rather than using algebraic connectivity or modularity, we use:
- Observability measures to ensure each partition can be monitored
- Controllability metrics to maintain control authority
- Stability indicators to preserve dynamic behavior
2. Full NDAE Modeling
We consider the complete $9^{\text{th}}$-order power system model including:
- Synchronous generator dynamics
- PV plant inverter controls
- Motor load characteristics
- Power flow constraints
3. Scalable Algorithms
The submodular structure enables efficient greedy algorithms that scale to large networks (we demonstrate on 2000-bus systems).
Example: 9-Bus Test System
We demonstrate the approach on a modified WSCC 9-bus system with integrated PV plants. The algorithm successfully partitions the network into three coherent subsystems:
- Subsystem 1: PV-dominated region with high renewable penetration
- Subsystem 2: Mixed generation with conventional and renewable sources
- Subsystem 3: Load-heavy area requiring careful voltage control
Each partition maintains strong internal observability while minimizing inter-partition coupling.
Summary
By embedding control theory into network partitioning, we can create more robust and responsive power systems. The submodular optimization approach provides both theoretical guarantees and practical scalability—essential for managing tomorrow’s renewable-heavy grids.
This work will be submitted to PSCC 2026, and I’m excited to share more detailed results as they develop!