Sensor Placement in District Heating Networks Using Frequency-Domain Gramians

District heating networks (DHNs) are essential in providing efficient heating services to urban areas through networked pipes. The performance of these systems critically depends on the strategic placement of thermal storage buffers (actuators) and temperature sensors throughout the network. Due to the inherent slow dynamics of thermal transport, these systems exhibit significant delays and periodic behaviors that necessitate time-varying analysis approaches. This paper presents a frequency-domain framework for optimal actuator and sensor placement in DHNs, focusing on metrics derived from frequential Gramians. We provide rigorous analysis of two key metrics, namely the trace and log-determinant of the frequential Gramian, establishing submodularity properties and performance guarantees for greedy selection algorithms. Our theoretical framework naturally handles both the periodic nature of DHNs and their slow transients, outperforming standard approaches in estimation accuracy.