[Paper Review] Dynamic Optimal Power Flow in Microgrids using the Alternating Direction Method of Multipliers

Paul Scott, Sylvie Thiébaux|arXiv (Cornell University)|Oct 29, 2014

Microgrid Control and Optimization16 references11 citations

TL;DR

This paper proposes a distributed dynamic optimal power flow (D-OPF) method for microgrids using the Alternating Direction Method of Multipliers (ADMM) with enhanced line models and a two-stage approach to handle discrete decisions and uncertainty. It achieves near-optimal solutions in fast, receding-horizon compatible timescales, enabling practical deployment of decentralized smart grid control.

ABSTRACT

Smart devices, storage and other distributed technologies have the potential to greatly improve the utilisation of network infrastructure and renewable generation. Decentralised control of these technologies overcomes many scalability and privacy concerns, but in general still requires the underlying problem to be convex in order to guarantee convergence to a global optimum. Considering that AC power flows are non-convex in nature, and the operation of household devices often requires discrete decisions, there has been uncertainty surrounding the use of distributed methods in a realistic setting. This paper extends prior work on the alternating direction method of multipliers (ADMM) for solving the dynamic optimal power flow (D-OPF) problem. We utilise more realistic line and load models, and introduce a two-stage approach to managing discrete decisions and uncertainty. Our experiments on a suburb-sized microgrid show that this approach provides near optimal results, in a time that is fast enough for receding horizon control. This work brings distributed control of smart-grid technologies closer to reality.

Motivation & Objective

• To address the challenge of decentralized, privacy-preserving optimal power flow in microgrids with realistic network and load models.
• To extend ADMM-based D-OPF to handle non-convex AC power flows, discrete household decisions, and uncertainty in renewable generation and load.
• To enable real-time, receding-horizon control by ensuring fast solution times while maintaining solution quality.
• To develop a two-stage pricing mechanism that incentivizes households to correct for local uncertainty and manage discrete variables effectively.
• To evaluate the method on a realistic suburb-sized microgrid with distributed PV and battery storage.

Proposed method

• The paper formulates the D-OPF problem over a multi-time-step horizon within a receding-horizon control framework to manage time-coupled components.
• It employs ADMM to decompose the global optimization problem across buses or network components, enabling distributed computation and preserving privacy.
• More accurate AC power flow models are used instead of simplified DC approximations to improve solution realism and accuracy.
• A two-stage approach is introduced: the first stage uses a relaxed problem with penalty functions to manage discrete variables, and the second stage adjusts pricing to correct for uncertainty and enforce consistency.
• The method uses a regularized pricing (RP) mechanism to align household incentives with system-wide cost minimization, especially under solar irradiance variability.
• The algorithm is tested on a 70-bus microgrid with randomly deployed 2kW PV systems and 2kWh batteries, using realistic solar irradiance profiles.

Experimental results

Research questions

• RQ1 Can ADMM-based distributed D-OPF achieve near-optimal solutions with realistic AC power flow models and fast enough convergence for receding-horizon control?
• RQ2 How can discrete household decisions (e.g., battery charging, appliance scheduling) be effectively managed within a distributed optimization framework?
• RQ3 What pricing mechanism can incentivize households to respond to uncertainty in local renewable generation without compromising system-wide optimality?
• RQ4 How does performance degrade under solar irradiance uncertainty, and can the two-stage approach mitigate this?
• RQ5 To what extent can the method be scaled or adapted to larger or more complex systems, including industrial loads and network topology changes?

Key findings

• The proposed method achieves near-optimal solutions in fast solve times, making it suitable for receding-horizon control in real-time microgrid operation.
• When solar output was lowered by 20%, generation costs increased by 8–10% relative to the original solution, demonstrating sensitivity to uncertainty.
• Function 0 of the RP method performed 1% better on average and increased household charges in line with higher generation costs, improving budget balance.
• Function 3 showed minimal response to increased costs, indicating poor incentive alignment, while Function 0 effectively leveraged excess solar when output was raised by 20%, reducing overall costs by ~8%.
• The penalty parameter α in the RP mechanism can be tuned to enforce compliance and support market budget balance, though it cannot distinguish between gaming and legitimate uncertainty.
• Batteries provide greater flexibility in handling local uncertainty, suggesting that storage integration enhances system robustness under imperfect forecasts.