Real-Time Network Reconfiguration for Minimizing Power Losses in Dynamic Distribution Grids

Core Concepts

The authors propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings, where the objective function is submodular. They apply these algorithms to two power system applications: fast-timescale demand response and real-time distribution network reconfiguration.

Abstract

The authors consider the problem of online dynamic submodular optimization, where the goal is to provide round optimal binary decisions while the objective function is time-varying and unknown at the time decisions have to be made. They propose two types of algorithms: (1) greedy approaches that solve approximations of the previous round's objective function, and (2) a projected gradient-based approach using the continuous and convex Lovász extension of submodular functions. For the greedy approaches, the authors first consider the online submodular greedy algorithm (OSGA) which solves to optimality an approximation of the previous round loss function. They extend OSGA to a generic approximation function. They show that OSGA has a dynamic regret bound similar to the tightest bounds in online convex optimization with respect to the time horizon and the cumulative round optimum variation. For instances where no approximation exists or a computationally simpler implementation is desired, the authors design the online submodular projected gradient descent (OSPGD) by leveraging the Lovász extension. They obtain a regret bound that is akin to the conventional online gradient descent (OGD). The authors numerically evaluate the performance of their approaches in two power system applications: Fast-timescale demand response: OSPGD is used to dispatch demand response resources for frequency regulation, outperforming a previous approach. Real-time distribution network reconfiguration: OSGA is applied to reconfigure the distribution network in real-time to minimize active power losses, leveraging a weakly-meshed network approximation. The authors show that their algorithms achieve sublinear dynamic regret, implying that the time-averaged regret vanishes as the time horizon increases.

Stats

The active and reactive power demand at bus i and time t are denoted as pi,t ≥ 0 and qi,t ≥ 0, respectively. The active and reactive power flowing from node i to j at time t are denoted as Pij,t ∈ R and Qij,t ∈ R, respectively. The apparent power in line ij at time t is denoted as Aij,t = Pij,t + jQij,t. The voltage at node i is denoted as vi ∈ C, the current flowing in line ij is denoted as Iij ∈ C, and the admittance of line ij is denoted as yij ∈ C.

Quotes

"To mitigate incidents, the system operator can preemptively configure the distribution network by altering its topology. Remotely-activated switches allow fast network reconfiguration (NR) and can be used to adapt to the load demand in real-time, viz., to prevent line congestion or to reduce active power losses." "Because (19) is submodular, and can be solved to optimality in polynomial time using a MST algorithm like Prim's [33] over the WMN, we apply our OSGA for online reconfiguration."

Key Insights Distilled From

Online Dynamic Submodular Optimization

by Antoine Lesa... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2306.10835.pdf

Deeper Inquiries

How could the proposed algorithms be extended to handle uncertainty in the power system parameters, such as load forecasting errors or renewable generation intermittency

To handle uncertainty in power system parameters, such as load forecasting errors or renewable generation intermittency, the proposed algorithms can be extended in the following ways: Stochastic Optimization: Introduce stochastic optimization techniques to model the uncertainty in parameters probabilistically. This can involve using scenario-based approaches, stochastic programming, or robust optimization to account for variations in load forecasts and renewable generation. Online Learning: Implement online learning algorithms that adapt to changing parameters in real-time. Techniques like online convex optimization with bandit feedback can be used to make decisions based on limited and noisy information. Scenario Analysis: Incorporate scenario analysis to evaluate the performance of the algorithms under different possible scenarios. By considering a range of potential parameter values, the algorithms can be designed to be robust to uncertainties. Adaptive Control: Implement adaptive control strategies that adjust the algorithm's parameters based on the observed discrepancies between predicted and actual values. This adaptive approach can help the algorithms react dynamically to changing conditions. By incorporating these extensions, the algorithms can become more resilient to uncertainties in power system parameters, ensuring robust performance in real-world applications.

What are the potential trade-offs between the computational complexity and the performance guarantees of the greedy and projected gradient-based approaches in practical power system applications

The potential trade-offs between computational complexity and performance guarantees of the greedy and projected gradient-based approaches in practical power system applications are as follows: Greedy Approach: Computational Complexity: The greedy approach involves solving approximations of the objective function in each round, which can be computationally intensive for large-scale systems with numerous decision variables. Performance Guarantee: The greedy approach provides a straightforward way to find a locally optimal solution at each step, but it may not always guarantee the best overall solution due to its myopic nature. Projected Gradient-Based Approach: Computational Complexity: The projected gradient descent approach involves performing a single gradient descent step, which is computationally efficient and scalable for large systems. Performance Guarantee: The projected gradient-based approach leverages the convexity of the Lovász extension to ensure convergence to a global optimum, providing stronger performance guarantees in terms of optimality. In practical power system applications, the choice between the two approaches depends on the system's size, the desired level of optimality, and the available computational resources. The greedy approach may be suitable for smaller systems where computational resources are limited, while the projected gradient-based approach is more appropriate for larger systems requiring stronger performance guarantees.

Could the online network reconfiguration problem be formulated as a multi-objective optimization problem to simultaneously minimize power losses and improve voltage profiles or other operational metrics

The online network reconfiguration problem can be formulated as a multi-objective optimization problem to simultaneously minimize power losses and improve voltage profiles or other operational metrics by considering the following: Objective Functions: Minimize Power Losses: The primary objective can be to minimize active power losses in the network, as in the current formulation. Improve Voltage Profiles: Another objective can be to optimize voltage profiles by minimizing voltage deviations or ensuring voltage stability across the network. Operational Metrics: Additional objectives can include improving system reliability, reducing line congestion, or optimizing reactive power flow. Multi-Objective Optimization: Use multi-objective optimization techniques such as weighted sum methods, Pareto optimization, or goal programming to balance the trade-offs between different objectives. Define appropriate weightings for each objective based on the system operator's priorities and constraints. Constraint Handling: Incorporate constraints related to voltage limits, line capacities, and network radiality to ensure the feasibility of the solutions. Develop constraint-handling mechanisms to address conflicting objectives and ensure that the solutions are practical and implementable. By formulating the network reconfiguration problem as a multi-objective optimization task, system operators can make more informed decisions that consider a broader range of performance metrics and operational goals simultaneously.