Extended Power Flow Model of Bus Reactive Power Margin and Its Fast Algorithm

The maximum bus reactive power condition is given in the paper, which is deduced from the nature of Jacobian matrix singularity when bus reactive power reaching its limits. The extended power flow equations is also given, and the solution of the equations is just the power flow solution when bus reactive power reaching its limits. A mixed Newton algorithm which based on Broyden row modification is proposed in the paper. To avoid explicit calculating the derivative of the maximum bus reactive power condition, Broyden row modification method is used to approximate it, so the computation burden is deduced significantly. Numerical test in two actual systems and several IEEE test systems show that the proposed method can obtain bus reactive power margin only once extended power flow calculation needed, has fast calculation speed and as robust as QV curve method.