Distributed Optimal Power Flow for Smart Microgrids (1211.5856v5)

Abstract: Optimal power flow (OPF) is considered for microgrids, with the objective of minimizing either the power distribution losses, or, the cost of power drawn from the substation and supplied by distributed generation (DG) units, while effecting voltage regulation. The microgrid is unbalanced, due to unequal loads in each phase and non-equilateral conductor spacings on the distribution lines. Similar to OPF formulations for balanced systems, the considered OPF problem is nonconvex. Nevertheless, a semidefinite programming (SDP) relaxation technique is advocated to obtain a convex problem solvable in polynomial-time complexity. Enticingly, numerical tests demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex OPF. To ensure scalability with respect to the number of nodes, robustness to isolated communication outages, and data privacy and integrity, the proposed SDP is solved in a distributed fashion by resorting to the alternating direction method of multipliers. The resulting algorithm entails iterative message-passing among groups of consumers and guarantees faster convergence compared to competing alternatives

• The paper introduces an SDP relaxation method that converts the nonconvex OPF problem in unbalanced microgrids into a convex formulation for global optimality.
• It employs a distributed ADMM framework that partitions the microgrid into local control areas, enabling parallel solving and efficient convergence.
• Numerical tests on IEEE feeders validate the approach by minimizing power losses and costs, consistently yielding rank-1 optimal solutions.

Distributed Optimal Power Flow for Smart Microgrids

The paper "Distributed Optimal Power Flow \ for Smart Microgrids" by Emiliano Dall'Anese, Hao Zhu, and Georgios B. Giannakis presents a semidefinite programming (SDP) approach for solving the Optimal Power Flow (OPF) problem in unbalanced microgrids. Microgrids are critical components of modern electrical networks that include distributed generation (DG), energy storage, and local loads, operating either connected to the main grid or in isolation.

Key Contributions and Methodology

The OPF problem for microgrids aims to minimize power distribution losses or the cost of power procurement from the grid and local DG units while ensuring proper voltage regulation. The OPF problem is inherently nonconvex due to the nonlinear relationship between voltages and the complex power at each node. Traditional methods often return suboptimal solutions and may not guarantee global optimality. To address these challenges, the authors propose using SDP relaxation techniques to reformulate the OPF problem into a convex one, which allows for solving it in polynomial time.

The main contributions of the paper can be summarized as follows:

1. SDP Relaxation for Unbalanced Microgrids: The authors introduce an SDP relaxation of the nonconvex OPF problem, which is then solved to find globally optimal solutions. The relaxed problem eliminates the rank constraint of the original nonconvex problem, enabling the use of standard SDP solvers.
2. Distributed Solution Using ADMM: To ensure scalability, the authors present a distributed solution based on the Alternating Direction Method of Multipliers (ADMM). The microgrid is partitioned into smaller areas, each managed by a local controller (LC). The ADMM framework enables these controllers to solve local subproblems and iteratively exchange information with neighboring controllers to find the global solution.
3. Handling Unbalanced Systems: The methodology addresses the unique challenges presented by unbalanced systems, such as unequal phase loads and different conductor spacings, which are common in real-world distribution networks.
4. Numerical Validation: The approach is validated through numerical tests on the IEEE 37-node test feeder and a 10-node microgrid. The results demonstrate that the proposed SDP relaxation consistently finds rank-1 (global optimal) solutions, validating the method's efficacy.

Numerical Results

Some notable numerical results include:

• The SDP-based method successfully obtained globally optimal solutions for the test feeder configurations, maintaining rank-1 solutions.
• Comparisons between centralized and distributed architectures show the distributed ADMM-based approach achieving significant computational efficiency and convergence speed.
• The power losses and costs were effectively minimized, and the DG units' active power generations were appropriately dispatched based on cost considerations.

For instance, in the IEEE 37-node test feeder:

• Power Losses: When $c_s = c_0$, power losses were minimized at 36.60 kW. As $c_s$ increases, the DG units reduce output, slightly increasing losses.
• Cost of Supplied Power: The cost varied significantly based on $c_s/c_0$, with a notable shift in DG utilization patterns as unit costs increased.
• Rank-1 Solutions: The method consistently found rank-1 solutions, affirming the global optimality of the solutions found by the SDP relaxation.

Implications and Future Directions

The proposed SDP-based approach has significant implications for the future of smart microgrid management:

• Scalability: The distributed ADMM methodology ensures scalability and real-time responsiveness, critical for handling large and dynamic microgrid systems.
• Robustness and Privacy: The decentralized nature of the approach enhances robustness against isolated failures and supports data privacy by limiting the extent of data sharing.
• Global Optimality: Achieving global optimality in OPF ensures the most efficient operation of microgrids, reducing operational costs and improving energy reliability.

Moving forward, several areas can be explored to extend and refine the presented methodology:

• Electric Vehicles and Storage Integration: Expanding the framework to incorporate the operational dynamics of electric vehicles and large-scale battery storage systems.
• Dynamic Operation and Forecasting: Incorporating dynamic models and forecasting to handle time-varying loads and generation patterns.
• Enhanced Coordination: Development of advanced coordination protocols that further reduce communication overhead and enhance convergence rates.

In summary, this paper lays a robust foundation for addressing OPF in unbalanced microgrid setups using SDP and distributed optimization techniques, setting a precedent for future research and application in smart grid technologies.