Scalable scheduling of energy control systems

Truong X. Nghiem, R. Mangharam
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引用次数: 1

Abstract

Peak power consumption is a universal problem across energy control systems in electrical grids, buildings, and industrial automation where the uncoordinated operation of multiple controllers result in temporally correlated electricity demand surges (or peaks). While there exist several diferent approaches to balance power consumption by load shifting and load shedding, they operate on coarse grained time scales and do not help in de-correlating energy sinks. The Energy System Scheduling Problem is particularly hard due to its binary control variables. Its complexity grows exponentially with the scale of the system, making it impossible to handle systems with more than a few variables. We developed a scalable approach for fine-grained scheduling of energy control systems that novelly combines techniques from control theory and computer science. The original system with binary control variables are approximated by an averaged system whose inputs are the utilization values of the binary inputs within a given period. The error between the two systems can be bounded, which allows us to derive a safety constraint for the averaged system so that the original system's safety is guaranteed. To further reduce the complexity of the scheduling problem, we abstract the averaged system by a simple single-state single-input dynamical system whose control input is the upper-bound of the total demand of the system. This model abstraction is achieved by extending the concept of simulation relations between transition systems to allow for input constraints between the systems. We developed conditions to test for simulation relations as well as algorithms to compute such a model abstraction. As a consequence, we only need to solve a small linear program to compute an optimal bound of the total demand. The total demand is then broken down, by solving a linear program much smaller than the original program, to individual utilization values of the subsystems, whose actual schedule is then obtained by a low-level scheduling algorithm. Numerical simulations in Matlab show the e ectiveness and scalability of our approach.
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能源控制系统的可伸缩调度
峰值电力消耗是电网、建筑物和工业自动化中的能源控制系统中普遍存在的问题,其中多个控制器的不协调操作导致临时相关的电力需求激增(或峰值)。虽然有几种不同的方法可以通过负载转移和减载来平衡电力消耗,但它们都是在粗粒度的时间尺度上运行的,并且无助于去相关的能量汇。能源系统调度问题由于其二元控制变量而显得尤为困难。它的复杂性随着系统的规模呈指数级增长,使得处理具有多个变量的系统变得不可能。我们开发了一种可扩展的方法,用于细粒度的能源控制系统调度,该方法新颖地结合了控制理论和计算机科学的技术。用一个平均系统来近似具有二元控制变量的原始系统,该系统的输入是给定周期内二元输入的利用值。两个系统之间的误差是有界的,这使得我们可以推导出平均系统的安全约束,从而保证原系统的安全性。为了进一步降低调度问题的复杂性,我们将平均系统抽象为一个简单的单状态单输入动态系统,其控制输入为系统总需求的上界。这个模型抽象是通过扩展过渡系统之间的模拟关系的概念来实现的,以允许系统之间的输入约束。我们开发了测试模拟关系的条件以及计算这种模型抽象的算法。因此,我们只需要求解一个小的线性程序来计算总需求的最优界。然后,通过求解一个比原方案小得多的线性规划,将总需求分解为子系统的个别利用值,并通过低级调度算法得到子系统的实际调度。Matlab中的数值仿真表明了该方法的有效性和可扩展性。
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