Towards multiobjective optimization and control of smart grids

Abstract: The rapid uptake of renewable energy sources in the electricity grid leads to a demand in load shaping and flexibility. Energy storage devices such as batteries are a key element to provide solutions to these tasks. However, typically a trade-off between the performance related goal of load shaping and the objective of having flexibility in store for auxiliary services, which is for example linked to robustness and resilience of the grid, can be observed. We propose to make use of the concept of Pareto optimality in order to resolve this issue in a multiobjective framework. In particular, we analyse the Pareto frontier and quantify the trade-off between the non-aligned objectives to properly balance them.

• The paper introduces a multiobjective optimization framework integrating energy storage to achieve both peak shaving and grid flexibility.
• It employs a nonlinear MPC and ADMM for scalable, distributed optimization, validated through numerical simulations with real-world data.
• Sensitivity analysis on battery SOC and tube constraints reveals trade-offs on the Pareto frontier, providing actionable insights for smart grid operations.

Multiobjective Optimization and Control in Smart Grids

The paper "Towards multiobjective optimization and control of smart grids" (1907.05826) addresses the integration of energy storage systems, such as batteries, within smart grids. It focuses on leveraging multiobjective optimization techniques to resolve trade-offs between peak shaving and providing grid flexibility. The research utilizes Pareto optimality to analyze these competing objectives and demonstrates how a Model Predictive Control (MPC) framework can manage these trade-offs efficiently.

Introduction and Problem Formulation

The core problem addressed in this paper is the integration of energy storage devices into smart grids to balance power loads while maintaining flexibility for auxiliary services. With the increasing prevalence of renewable energy sources, power systems face volatile demand and supply, necessitating efficient storage and load management strategies.

System Dynamics and Objectives

The paper models residential energy systems equipped with solar panels and batteries as individual subsystems connected via a central entity. The primary objectives are:

1. Peak Shaving: Flattening energy demand to reduce fluctuations, facilitating easier and cost-effective energy management.
2. Flexibility: Introducing tube constraints to provide flexibility, allowing for responsive adjustments to power demands and supply deviations.

Mathematical Modeling

The paper formulates the problem using a nonlinear MPC framework, considering constraints on state variables such as the State Of Charge (SOC) of batteries and charging/discharging rates. The optimization problem is structured as a multiobjective task, with the Pareto frontier used to balance the competing objectives.

Multiobjective Optimization Framework

The paper introduces a scalarized optimization problem, leveraging Alternating Direction Method of Multipliers (ADMM) for distributed optimization. ADMM is suited to handle large-scale systems by decomposing tasks across subsystems for efficient computation. The Pareto frontier is explored to characterize trade-offs and achieve efficient points in the system.

ADMM Implementation

The implementation uses ADMM to solve the scalarized optimization problem, ensuring scalability and plug-and-play capability of the distributed systems. The paper details explicit steps within the ADMM framework, focusing on minimizing aggregated power demand deviations and tube constraint violations.

Numerical Simulations and Results

Simulation results highlight the impact of varying the weight of each objective in the scalarization. It demonstrates how different configurations lead to different trade-offs on the Pareto frontier. The performance is evaluated using real-world data, showcasing the effectiveness of the proposed framework in managing grid flexibility while achieving peak shaving.

Pareto Frontier and Sensitivity Analysis

The Pareto frontier is characterized by analyzing the efficiency of solutions across varying objective weights. This section also provides a sensitivity analysis regarding the initial SOC and tube size, illustrating how these factors influence the optimization outcome.

Proper Optimality

The paper applies the concept of proper optimality, quantifying the cost of trade-offs between objectives. This helps in structured decision-making, providing insights into the implications of a specific choice on the system performance.

Conclusion

The paper successfully embeds the problem of energy storage management within smart grids into a multiobjective framework. By employing Pareto optimality and ADMM, the research offers a robust methodology for optimizing system performance amid conflicting goals. This framework enables smart grids to efficiently accommodate renewable energy sources, manage load, and maintain grid resilience.

Future work could extend the model to explore advanced prediction methods for load forecasting and integrate the framework with controllable loads for further optimization capabilities. The research opens pathways for enhancing smart grid operations through sophisticated optimization strategies.