We develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance constraint. Models with a few hundred scenarios are relatively tractable; for larger models, we demonstrate how a Lagrangian relaxation scheme provides improved results. To further accelerate the Lagrangian scheme, we embed the progressive hedging algorithm within the subgradient iterations of the Lagrangian relaxation. We investigate several enhancements of the progressive hedging algorithm, and find bundling of scenarios results in the best bounds. Finally, we provide a generalization for how our analysis extends to a microgrid with multiple batteries and photovoltaic generators.

我们开发了一个随机优化模型来调度混合太阳能电池存储系统。超过承诺的太阳能可用于为电池充电，而低于承诺的电力则通过对电池放电来满足。我们通过使用联合机会约束来确保可靠的操作。几百个场景的模型相对容易处理；对于较大的模型，我们演示了拉格朗日松弛方案如何提供改进的结果。为了进一步加速拉格朗日方案，我们在拉格朗日松弛的次梯度迭代中嵌入了渐进对冲算法。我们研究了渐进对冲算法的几种增强功能，并发现场景的捆绑导致了最佳界限。最后，