- The paper develops a distributed ADMM-based framework that decomposes dynamic optimal power flow problems into tractable subproblems for microgrids.
- It employs multiple power flow models and a two-stage Relax and Price method to handle non-convex AC flows and discrete household decisions effectively.
- Experiments on a 70-bus microgrid with 3,674 agents show near-optimal performance with the AC model achieving only a 0.008% error margin.
Dynamic Optimal Power Flow in Microgrids using the Alternating Direction Method of Multipliers
Introduction
This paper explores the dynamic optimal power flow (D-OPF) problem in microgrids using the Alternating Direction Method of Multipliers (ADMM). The focus is on addressing non-convexities arising from AC power flows and discrete household device operations, which are typical in realistic power systems. The study extends prior methodologies to incorporate realistic line and load models, adopting a two-stage approach for managing discrete decisions and uncertainties.
Methodology
Alternating Direction Method of Multipliers (ADMM)
ADMM is employed to decompose the D-OPF problem into more tractable subproblems by leveraging network partitioning. Each component of the power system is solved individually, allowing the global problem to converge through iterations over local solutions. The method includes a design for updating primal and dual residuals to ensure convergence to the Karush-Kuhn-Tucker (KKT) conditions.
Power Flow Models
Various power flow models are considered, including AC, quadratic constraints (QC), and dist-flow (DF). The paper demonstrates the efficacy of the AC model for providing solutions close to global optima while satisfying Ohm's law. Comparisons show that while simpler models like DC flow are computationally faster, they lack accuracy in heavily congested networks.
Discrete Decisions and Pricing
A two-stage framework, leveraging approaches like Relax and Price (RP), is introduced to handle discrete variables and local uncertainties. This mechanism involves a negotiation stage where problems are relaxed, followed by a decision stage ensuring integer feasibility through localized optimization. Furthermore, the study evaluates economic models for pricing uncertainties in solar output and consumer loads.
Experimental Setup
The experiments were conducted on a meshed microgrid inspired by a 70-bus 11kV benchmark network. This setting simulates approximately 3,674 household agents, each with a set of independent components, such as shiftable loads, generators, and batteries. The system uses a 24-hour time horizon, divided into 15-minute intervals, resulting in over 2 million variables per problem instance.
Results
Power Flow Model Comparison
- AC Model: Near-optimal with 0.008% margin of error.
- QC Model: Provides a robust lower bound.
- K Model: Faster convergence but results in significant inaccuracies, with a 4.726% deviation from optimal.
- DC Model: Underestimates significantly due to ignoring line losses.
Discrete Decision Management
All investigated methods for handling binary decisions (RP, RD, UR) yielded operational results within 1% of the relaxed problem's lower bound. The RP approach was particularly preferred for its ability to incorporate pricing mechanisms for uncertainty management, offering a pragmatic balance between solution quality and computational efficiency.
Implications and Future Work
The study provides a scalable solution for dynamic energy management in microgrids, with implications for real-time power system operation, especially with the increasing prevalence of distributed energy resources. Future work could explore fine-tuning penalty parameters for demand-side management, further parallelizing the problem decomposition across time steps, and embedding second-order information to improve convergence rates. Additionally, the potential robustness against market gaming and the handling of larger discrete decisions remain open areas for exploration.
Conclusion
By furnishing a distributed methodology that closely aligns with real-world operational constraints and system requirements, this research brings distributed control in smart grids closer to practical realization. This approach has the potential to significantly improve cost-efficiency and reliability in decentralized power systems.
