We consider a linear power flow model with interval-bounded nodal power injections and limited line power flows. We determine the minimal number of power injections to control based on a minimal set of measurements, such that the overall system is feasible for all assignments of the non-controlled power injections. For the important case where the possible measurements are the nodal power injections, we show that the problem can be solved efficiently as a mixed-integer linear program (MILP). When also line power flows are considered as potential measurements, we derive an iterative, greedy algorithm that provides a feasible, but potentially conservative solution. We apply the developed algorithms to both a small microgrid and a modified version of the IEEE 118 bus test power system. We show that in both cases a sparse solution in terms of the number of required controllers and measurements can be obtained. Moreover, the number of required measurements can be reduced significantly if line flow measurements are considered additionally to nodal power injections.

中文翻译：

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用于线性潮流的控制器和传感器的最小集合

我们考虑具有区间有界节点功率注入和有限线路功率流的线性功率流模型。我们根据最小的一组测量值确定要控制的最小功率注入次数，这样整个系统对于非受控功率注入的所有分配都是可行的。对于可能的测量是节点功率注入的重要情况，我们表明该问题可以作为混合整数线性程序 (MILP) 有效解决。当线路潮流也被视为潜在的测量时，我们推导出一个迭代的贪婪算法，它提供了一个可行但可能保守的解决方案。我们将开发的算法应用于小型微电网和 IEEE 118 总线测试电源系统的修改版本。我们表明，在这两种情况下，可以获得所需控制器和测量数量方面的稀疏解决方案。此外，如果除了节点功率注入之外还考虑线路流量测量，则可以显着减少所需测量的数量。