Abstract: Based on the theory of Grbner basis,apower flow problem,which is a polynomial equation system problem,is converted into an equivalent eigenvalue/vector problem.The effectiveness and accuracy of the proposed method is better than an elimination method,which is the only method available so far.The proposed method can yield all solutions of the system without any singular matrix problem.A two-machine five-bus system never before solved by elimination methods is studied as an example,whose eight solutions are obtained and the PV curves,which are more complete than those obtained by a continuous power flow method,are described to demonstrate the effectiveness of the proposed method.