Solving of interval DC power flow using interval Hull algorithm with preconditioning

With intermittent sources integrated into the power grid, power flows of the power grid are getting stochastic. Considering the uncertainty problem of DC power flow in the high voltage transmission system, this paper recommends an interval Hull algorithm with preconditioning to solve the interval DC power flow. Firstly, the diagonal dominant interval coefficient matrix is formed by preconditioning, then the H-matrix is obtained using the interval Hull algorithm. Different approximation methods are employed for the comparison matrix of H-matrix to improve precision. And the upper and lower bound of the distribution of interval DC power flow is obtained with the iterative method. The interval Hull algorithm and Monte Carlo algorithm are compared in the 9-bus test system, the result of which shows that the uncertainty in grid parameters is the main cause of errors. Furthermore, the Hull algorithm with preconditioning, the interval Hull method, the Krawczyk operator iteration method and the Gauss elimination method are compared in terms of accuracy and computing time on an IEEE 57-bus and an IEEE 118-bus test system, respectively. It is shown that the Hull method with preconditioning has the best accuracy, and the time complexity is far lower than that of the Monte Carlo algorithm.