State Estimation of District Heating Network Based on Kalman Filter

摘要

Since the beginning of the 20th century,district heating(DH)has been utilized widely in many European Countries such as Germany,Finland,Belgium,Sweden,Denmark and Holland.In Finland,approximately half of the heating market was covered by DH by 2009.For better use of the district heating,real-time monitoring of the water flows,temperatures and heat losses plays an important role in managing and operating DH network.In this paper,the state of a dual pipe DH network,such as water flows,temperatures and heat losses are estimated by a model based on customer measurements.Assuming a tree-like topology for the network,the flow equations form an overdetermined linear system can be solved in the least squares sense based on customer flow measurements.After that,the estimated temperature and heat losses for all the pipes can be formulated as an overdetermined system that can again be determined by least squares sense based on customer temperature measurements and the computed water flows.Afterwards,the estimated water temperature and heat loss can be substituted back to re-compute the combined heat loss factor S in each pipe,we estimate the heat loss factor using the Kalman filter based on the recomputed S value.Additionally,the uncertainties of the predicted state for the estimated S are obtained in form of covariance matrices that can be used to assess the accuracy of the state estimate.Large inaccuracies may indicate problems in the network or the measurement system.The Kalman filter updates the state estimate for consecutive hours in two-steps: 1)forms a prediction of the current state variables and their uncertainties; and 2)corrects the estimates based on measurements.Both the state estimation and the uncertainty analysis are illustrated with a small district heating network based on their hourly temperature and water flow measurements for 168 hourly time steps(one week).