Uncertainty Analysis of District Heating State Estimation Model

Tingting Fang and Risto Lahdelma


Uncertainty analysis, Error propagation, Analysis, management and modeling, District heating, Least squares estimation


The water flows, temperatures and heat losses in a district heating (DH) network can be estimated by a model based on customer measurements. In this paper, we analyze the uncertainty of the estimation model based on accuracy estimates of the measurements. We apply the error propagation formula to determine analytically the uncertainty in the linear water flow system. After that, we determine the uncertainties of the estimated temperatures and heat losses using the error propagation formula again to, this time based on the uncertainties of the water flow model and uncertainties in temperature measurements. For the second model we determine the sensitivity coefficients numerically. We illustrate the uncertainty computations with a small district heating network based on hourly temperature measurements and computed water flows for one time step.

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