This paper provides an experimentally validated optimal control approach based on a Hamilton–Jacobi–Bellman (HJB) model for optimising aggregated distributed energy resources across multiple energy carriers. The research incorporates nonlinear effects arising from storage degradation, conversion efficiency and self-discharge as well as multiple energy carrier storage. A semi-Lagrangian HJB solver was implemented on low-cost digital controllers, and integrated into a real fully functional cloud-based aggregation platform. The computational cost is kept at a minimum, enabling on-line computations on the low-cost controller, while maintaining a rigorous proof of convergence to the theoretical value function of the nonlinear, non-convex optimal control problem.

The controller links into a distributed optimal control platform that is using local as well as cloud-based information and performs all the computation and decision-making locally. The distributed controllers were tested and validated on site with an electrical and a thermal storage device. Experimental results confirm that the framework is practical, accommodates nonlinear effects and inaccurate external forecasts, has a small computational cost, is robust and can deliver significant cost benefits to the stakeholders.

本文提供了一种基于 Hamilton-Jacobi-Bellman (HJB) 模型的经过实验验证的最优控制方法，用于优化跨多个能源载体的聚合分布式能源。该研究结合了由存储退化、转换效率和自放电以及多能量载体存储引起的非线性效应。半拉格朗日 HJB 求解器在低成本数字控制器上实现，并集成到真正功能齐全的基于云的聚合平台中。计算成本保持在最低水平，从而能够在低成本控制器上进行在线计算，同时保持收敛到非线性、非凸最优控制问题的理论值函数的严格证明。

控制器连接到分布式优化控制平台，该平台使用本地和基于云的信息，并在本地执行所有计算和决策。分布式控制器通过电气和热存储设备在现场进行了测试和验证。实验结果证实该框架是实用的，适应非线性效应和不准确的外部预测，计算成本小，稳健并且可以为利益相关者带来显着的成本效益。