This thesis deals with the AC Load Flow Problem and the comparison of two different solution techniques. The basic solution used was the Newton Raphson method. The two methods used to solve for the corrections to the bus voltages are general matrix storage and nonzero element storage. In the general matrix all matrices are used with every element represented. In the non-zero routine, only nonzero entries in the YBUS and the Jacobian matrix are stored. Along with the non-zero routine, a form of sub-optimal ordering was used to make the inversion process faster. The execution times and storage requirements for seven examples are given. These results show the advantages of using a non-zero storage technique with respect to execution time as well as storage requirements. / Master of Science