Water System's Measurement Point Placement And State Estimation

The paper represents an algorithm for determination of minimum measurement set in water-system state estimation, which depends on the theory of observability-the water-system is observable if and only if it contains a full-rank spanning tree. After a brief description of observable theory in water-system , and how to convert the real pipe graph to the topological graph is presented in this paper , then the minimum measurement set is given by using of the algorithm of spanning tree and combining data structure and graphical theory . If there is no measurement point in the original system , the minimum measurement set can be achieved by the algorithm represented in this paper , whereas if there are some measurement points , which guarantees the whole or part of system observable , this algorithm can determine the maximal observable part and where measurement point should be added to guarantee the whole system's observability . At last, several common examples in water-system testify the results of this paper.After the determination of the minimum measurement set , a water system's numerical model is set up by the application of the graph theory in water-system ,then according to the measurement set given by measurement set its state is estimated . It converts the problem of state estimation to linear programming , at the same time it transforms the objective function from the sum of square error to the sum of the modulus of the error . At the end , the results of the test shows this algorithm can be used in state estimation by computer.